Academic Appointments

  • Emeritus Faculty, Acad Council, Mathematics

Administrative Appointments

  • Graduate Fellowship, National Science Foundation (1972 - 1975)
  • Sloan Postdoctoral Fellowship, Alfred P. Sloan Foundation (1979 - 1979)
  • MacArthur Prize Fellowship, MacArthur Foundation (1983 - 1988)
  • Fellow, Amer. Assoc. for Adv. of Science (1995 - 1995)
  • Guggenheim Fellowship, Guggenheim Foundation (1996 - 1996)
  • Fellow, American Mathematical Society (2012 - 2012)
  • Lecturer, University of California, Berkeley (1976 - 1978)
  • Assistant Professor, Courant Institute, New York University (1978 - 1980)
  • Professor, University of California, Berkeley (1980 - 1984)
  • Professor, University of California, San Diego (1984 - 1987)
  • Professor, Stanford University (1987 - 1992)
  • Bass Professor, Humanities and Sciences, Stanford University (1992 - Present)
  • Visiting Member, Institute for Advanced Study (1979 - 1980)
  • Spring Visiting Member, Institute for Advanced Study (1984 - 1984)
  • Visiting Professor, Courant Institute, New York University (1989 - 1990)
  • Distinguished Visiting Professor, Institute for Advanced Study (1992 - 1993)
  • Autumn Visiting Professor, Harvard University (1999 - 1999)
  • Autumn Eilenberg Chair, Columbia University (2009 - 2009)

Honors & Awards

  • Lobachevsky Medal and Prize, Russian Academy of Sciences and Kazan State University (2017)
  • Heinz Hopf Prize, ETH Zurich (2017)
  • Rolf Schock Prize in Mathematics, Royal Swedish Academy of Sciences (2017)
  • Wolf Prize in Mathematics, Wolf Foundation (2107)
  • Bocher Prize, American Mathematical Society (1989)

Boards, Advisory Committees, Professional Organizations

  • Editor, Journal of Differential Geometry
  • Editor, Communications in Analysis and Geometry
  • Editor, Calculus of Variations and PDE
  • Chair, Mathematics Department, Stanford University (2001 - 2004)
  • Member, Fachbeirat for Max Planck Institute for Gravitation (2004 - 2010)
  • Member, Scientific Advisory Committee of Mathematical Sciences Research Institute (2007 - 2012)
  • Co-Chair, Scientific Advisory Committee of Mathematical Sciences Research Institute (2009 - 2012)
  • Chair, Committee to choose director of Mathematical Sciences Research Institute (2012 - 2012)
  • Clay Senior Scholar, Park City Mathematics Institute (2013 - 2013)
  • Chair of review committee, National Center for Theoretical Sciences Hsinchu (2013 - 2013)
  • Member of Advisory Board, Institute of Mathematics Academia Sinica (2013 - 2013)
  • Program Committee and lecturer, Mathematical Congress of the Americas (2013 - 2013)
  • Organizer, Mathematical Sciences Research Institute program in Mathematical General Relativity (2013 - 2013)
  • Member, National Academy of Sciences (1991 - 1991)
  • Member, American Academy of Arts and Sciences (1988 - 1988)

Professional Education

  • Ph.D., Stanford University (1977)
  • B.S., University of Dayton (1972)

Contact

  • Academic
    schoen@math.stanford.edu
    University - Emeritus faculty Department: Mathematics Position: Emeritus Faculty, Acad Council
    • BLDG. 380 RM. 383-T
    • Stanford,  California  94305-2125 
    (650) 725-4066 (fax)

Additional Info

  • Mail Code: 2125

Links

All Publications

  • Existence and geometric structure of metrics on surfaces which extremize eigenvalues BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY Schoen, R. 2013; 44 (4): 777-807

    View details for DOI 10.1007/s00574-013-0034-6

    View details for Web of Science ID 000330963100011

  • Convexity of Reduced Energy and Mass Angular Momentum Inequalities ANNALES HENRI POINCARE Schoen, R., Zhou, X. 2013; 14 (7): 1747-1773

    View details for DOI 10.1007/s00023-013-0240-1

    View details for Web of Science ID 000325616900003

  • Minimal surfaces and eigenvalue problems Contemporaty Mathematics Schoen, R. M., Fraser, A. 2013; 599: 105-122
  • Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets COMMUNICATIONS IN MATHEMATICAL PHYSICS Huang, L., Schoen, R., Wang, M. 2011; 306 (3): 785-803

    View details for DOI 10.1007/s00220-011-1295-9

    View details for Web of Science ID 000294010400008

  • ON THE EXISTENCE OF HAMILTONIAN STATIONARY LAGRANGIAN SUBMANIFOLDS IN SYMPLECTIC MANIFOLDS AMERICAN JOURNAL OF MATHEMATICS Joyce, D., Lee, Y., Schoen, R. 2011; 133 (4): 1067-1092

    View details for Web of Science ID 000293044500008

  • The first Steklov eigenvalue, conformal geometry, and minimal surfaces ADVANCES IN MATHEMATICS Fraser, A., Schoen, R. 2011; 226 (5): 4011-4030

    View details for DOI 10.1016/j.aim.2010.11.007

    View details for Web of Science ID 000287460000004

  • CURVATURE, SPHERE THEOREMS, AND THE RICCI FLOW BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Brendle, S., Schoen, R. 2011; 48 (1): 1-32

    View details for Web of Science ID 000287007900001

  • Riemannian manifolds of positive curvature Proceedings of the International Congress of Mathematicians Schoen, R. M., Brendle, S. 2010
  • Gravitating opposites attract CLASSICAL AND QUANTUM GRAVITY Beig, R., Gibbons, G. W., Schoen, R. M. 2009; 26 (22)

    View details for DOI 10.1088/0264-9381/26/22/225013

    View details for Web of Science ID 000271090100017

  • Manifolds with 1/4-pinched curvature are space forms JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Brendle, S., Schoen, R. 2009; 22 (1): 287-307

    View details for Web of Science ID 000259723900008

  • Isoperimetric inequality for fiat surfaces Proceedings of the 13th International Workshop on Differential Geometry and Related Fields Schoen, R. M., Choe, J. 2009
  • Sphere theorems in geometry Geometry, analysis, and algebraic geometry: forty years of the Journal of Differential Geometry Schoen, R., Brendle, S. Int. Press. 2009 : 49–84
  • On static n-body configurations in relativity, 10 page preprint Classical and Quantum Gravity Schoen, R. M., Beig, R. 2009; 26: 7
  • A COMPACTNESS THEOREM FOR THE YAMABE PROBLEM JOURNAL OF DIFFERENTIAL GEOMETRY Khuri, M. A., Marques, F. C., Schoen, R. M. 2009; 81 (1): 143-196

    View details for Web of Science ID 000262728400003

  • Classification of manifolds with weakly 1/4-pinched curvatures ACTA MATHEMATICA Brendle, S., Schoen, R. M. 2008; 200 (1): 1-13

    View details for DOI 10.1007/s11511-008-0022-7

    View details for Web of Science ID 000254258200001

  • A generalization of Hawking's black hole topology theorem to higher dimensions COMMUNICATIONS IN MATHEMATICAL PHYSICS Galloway, G. J., Schoen, R. 2006; 266 (2): 571-576

    View details for DOI 10.1007/s00220-006-0019-z

    View details for Web of Science ID 000239148300011

  • On the asymptotics for the vacuum Einstein constraint equations JOURNAL OF DIFFERENTIAL GEOMETRY Corvino, J., Schoen, R. M. 2006; 73 (2): 185-217

    View details for Web of Science ID 000238234200001

  • The mathematics of general relativity: Problems and progress Sesquicentennial Conference of Mathematics at Washington University Schoen, R. AMER MATHEMATICAL SOC. 2006: 119–132

    View details for Web of Science ID 000235887900011

  • Minimal submanifolds in higher codimension Matematica Contemponlnea Schoen, R. M. 2006; 30: 169-199
  • Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Guan, B., Jian, H., Schoen, R. M. 2006; 595: 167-188

    View details for DOI 10.1515/CRELLE.2006.047

    View details for Web of Science ID 000239272500006

  • KIDs are non-generic ANNALES HENRI POINCARE Beig, R., Chrusciel, P. T., Schoen, R. 2005; 6 (1): 155-194

    View details for DOI 10.1007/s00023-005-0202-3

    View details for Web of Science ID 000227276300006

  • Mean curvature in geometry and general relativity Proceedings of the 2001 Clay Summer School Schoen, R. M. edited by Hoffman, D. 2005: 113–36
  • Special lagrangian submanifolds Proceedings of the 2001 Clay Summer School Schoen, R. M. edited by Hoffman, D. 2005: 655–66
  • The volume functional for Lagrangian submanifolds, Lectures on partial differential equations New Stud. Adv. Math Schoen, R. M. edited by Wolfson, J. Int. Press, Somerville, MA. 2003: 181–191
  • Minimizing area among Lagrangian surfaces: The mapping problem JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R., Wolfson, J. 2001; 58 (1): 1-86

    View details for Web of Science ID 000175058500001

  • Refined asymptotics for constant scalar curvature metrics with isolated singularities INVENTIONES MATHEMATICAE Korevaar, N., Mazzeo, R., Pacard, F., Schoen, R. 1999; 135 (2): 233-272

    View details for Web of Science ID 000078265700001

  • Recent proofs of the Riemannian Penrose conjecture in General Relativity Current developments in mathematics Schoen, R. M., Bray, H. Int. Press, Somerville, MA. 1999: 1–36
  • Minimizing volume among Lagrangian submanifolds Proc Symp Pure Math Schoen, R. M., Wolfson, J. edited by Shatah, J. 1999: 181–199
  • Theorems of Barth-Lefschetz type and Morse theory on the space of paths MATHEMATISCHE ZEITSCHRIFT Schoen, R., Wolfson, J. 1998; 229 (1): 77-89

    View details for Web of Science ID 000076244300005

  • Global existence theorems for harmonic maps to nonlocally compact spaces Comm Anal Geom Schoen, R. M., Korevaar, N. 1997; 5: 333-387
  • Lectures on Harmonic Maps Schoen, R. M., Yau, S. T. International Press Inc., Boston. 1997
  • Prescribed scalar curvature on the n-sphere CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Schoen, R., Zhang, D. 1996; 4 (1): 1-25

    View details for Web of Science ID A1996TH25000001

  • The effect of curvature on the behavior of harmonic functions and mappings Nonlinear Partial Differential Equations in Differential Geometry Schoen, R. M. edited by Hardt, R., Wolf, M. AMS. 1996: 127–185
  • ON THE CONFORMAL AND CR AUTOMORPHISM-GROUPS GEOMETRIC AND FUNCTIONAL ANALYSIS Schoen, R. 1995; 5 (2): 464-481

    View details for Web of Science ID A1995RK79400013

  • Lectures on Differential Geometry Yau, S. T., Schoen, R. M. International Press Inc., Boston. 1994
  • THE ROLE OF HARMONIC-MAPPINGS IN RIGIDITY AND DEFORMATION PROBLEMS OSAKA INTERNATIONAL CONF ON COMPLEX GEOMETRY AND RELATED TOPICS SCHOEN, R. M. MARCEL DEKKER. 1993: 179–200

    View details for Web of Science ID A1993BX36L00014

  • Sobolev spaces and harmonic maps for metric space targets Comm Anal Geom Schoen, R. M., Korevaar, N. 1993; 1: 561-659
  • HARMONIC MAPS INTO SINGULAR SPACES AND P-ADIC SUPERRIGIDITY FOR LATTICES IN GROUPS OF RANK-ONE PUBLICATIONS MATHEMATIQUES Gromov, M., Schoen, R. 1992: 165-246

    View details for Web of Science ID A1992LJ98100004

  • A report on some recent progress on nonlinear problems in geometry Surveys in Differential Geometry Schoen, R. M. 1991; 1: 204-241
  • On the number of constant scalar curvature metrics in a conformal class Differential Geometry Schoen, R. M. edited by Lawson, Tenenblat Longman Scientific and Technical. 1991: 311–320
  • THE EXISTENCE OF WEAK SOLUTIONS WITH PRESCRIBED SINGULAR BEHAVIOR FOR A CONFORMALLY INVARIANT SCALAR EQUATION COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS SCHOEN, R. M. 1988; 41 (3): 317-392

    View details for Web of Science ID A1988M972700004

  • CONFORMALLY FLAT MANIFOLDS, KLEINIAN-GROUPS AND SCALAR CURVATURE INVENTIONES MATHEMATICAE Schoen, R., Yau, S. T. 1988; 92 (1): 47-71

    View details for Web of Science ID A1988M670500002

  • Variational theory for the total scalar curvature functional for Riemannian metrics and related topics Topics in Calculus of Variations Schoen, R. M. edited by Giaquinta, M. Springer. 1988: 120–155
  • CONFORMAL METRICS WITH PRESCRIBED SCALAR CURVATURE INVENTIONES MATHEMATICAE Escobar, J. F., SCHOEN, R. M. 1986; 86 (2): 243-254

    View details for Web of Science ID A1986E189700003

  • Recent progress in geometric partial differential equations Proc ICM Schoen, R. M. 1986: 121–130
  • Positive harmonic functions on manifolds of negative curvature Annals of Math Schoen, R. M., Anderson, M. 1985; 121: 429-461
  • THE SPACE OF MINIMAL EMBEDDINGS OF A SURFACE INTO A 3-DIMENSIONAL MANIFOLD OF POSITIVE RICCI CURVATURE INVENTIONES MATHEMATICAE Choi, H. I., Schoen, R. 1985; 81 (3): 387-394

    View details for Web of Science ID A1985ASQ1300001

  • CONFORMAL DEFORMATION OF A RIEMANNIAN METRIC TO CONSTANT SCALAR CURVATURE JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R. 1984; 20 (2): 479-495

    View details for Web of Science ID A1984AKC1800011

  • On the isoperimetric inequality for minimal surfaces Ann Scuola Norm Sup Pisa Schoen, R. M., Li, P., Yau, S. T. 1984; 9: 237-244
  • Analytic aspects of the harmonic map problem Seminar on Nonlinear PDE Schoen, R. M. edited by Chern, S. S. Springer-Verlag. 1984: 321–358
  • LP AND MEAN-VALUE PROPERTIES OF SUBHARMONIC FUNCTIONS ON RIEMANNIAN-MANIFOLDS ACTA MATHEMATICA Li, P., Schoen, R. 1984; 153 (3-4): 279-301

    View details for Web of Science ID A1984ABL6200004

  • REGULARITY OF MINIMIZING HARMONIC MAPS INTO THE SPHERE INVENTIONES MATHEMATICAE Schoen, R., Uhlenbeck, K. 1984; 78 (1): 89-100

    View details for Web of Science ID A1984TS07500003

  • REGULARITY OF SIMPLY CONNECTED SURFACES WITH QUASICONFORMAL GAUSS MAP ANNALS OF MATHEMATICS STUDIES Schoen, R., Simon, L. 1983: 127-145

    View details for Web of Science ID A1983SB53200006

  • BOUNDARY-REGULARITY AND THE DIRICHLET PROBLEM FOR HARMONIC MAPS JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R., Uhlenbeck, K. 1983; 18 (2): 253-268

    View details for Web of Science ID A1983RF92700003

  • UNIQUENESS, SYMMETRY, AND EMBEDDEDNESS OF MINIMAL-SURFACES JOURNAL OF DIFFERENTIAL GEOMETRY SCHOEN, R. M. 1983; 18 (4): 791-809

    View details for Web of Science ID A1983SE89500009

  • THE EXISTENCE OF A BLACK-HOLE DUE TO CONDENSATION OF MATTER COMMUNICATIONS IN MATHEMATICAL PHYSICS Schoen, R., Yau, S. T. 1983; 90 (4): 575-579

    View details for Web of Science ID A1983RH82900010

  • ESTIMATES FOR STABLE MINIMAL-SURFACES IN 3 DIMENSIONAL MANIFOLDS ANNALS OF MATHEMATICS STUDIES Schoen, R. 1983: 111-126

    View details for Web of Science ID A1983SB53200005

  • Minimal surfaces and positive scalar curvature Proc ICM Schoen, R. M. 1982: 575–578
  • A LOWER BOUND FOR THE 1ST EIGENVALUE OF A NEGATIVELY CURVED MANIFOLD JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R. 1982; 17 (2): 233-238

    View details for Web of Science ID A1982PH26500003

  • COMPLETE 3 DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE ANNALS OF MATHEMATICS STUDIES Schoen, R., Yau, S. T. 1982: 209-228

    View details for Web of Science ID A1982RJ31900012

  • A REGULARITY THEORY FOR HARMONIC MAPS JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R., Uhlenbeck, K. 1982; 17 (2): 307-335

    View details for Web of Science ID A1982PH26500006

  • A REMARK ON MINIMAL HYPERCONES PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES Schoen, R. 1982; 79 (14): 4523-4524

    Abstract

    Let M be a minimal hypersurface in the sphere. It is shown that if the cone over M is a stable critical point for the area functional, then M admits a conformally equivalent metric with positive scalar curvature. This gives both topological and geometric restrictions on such hypersurfaces M.

    View details for Web of Science ID A1982NY24400009

    View details for PubMedID 16593217

  • ON THE GAUSS MAP OF COMPLETE-SURFACES OF CONSTANT MEAN-CURVATURE IN R3 AND R4 COMMENTARII MATHEMATICI HELVETICI Hoffman, D. A., Osserman, R., Schoen, R. 1982; 57 (4): 519-531

    View details for Web of Science ID A1982QF55900001

  • A NEW PROOF OF THE REGULARITY THEOREM FOR RECTIFIABLE CURRENTS WHICH MINIMIZE PARAMETRIC ELLIPTIC FUNCTIONALS INDIANA UNIVERSITY MATHEMATICS JOURNAL Schoen, R., Simon, L. 1982; 31 (3): 415-434

    View details for Web of Science ID A1982NW20800010

  • ON THE EXISTENCE OF HARMONIC DIFFEOMORPHISMS BETWEEN SURFACES INVENTIONES MATHEMATICAE Jost, J., Schoen, R. 1982; 66 (2): 353-359

    View details for Web of Science ID A1982NP79900011

  • PROOF OF THE POSITIVE MASS THEOREM .2. COMMUNICATIONS IN MATHEMATICAL PHYSICS Schoen, R., Yau, S. T. 1981; 79 (2): 231-260

    View details for Web of Science ID A1981LL40100005

  • REGULARITY OF STABLE MINIMAL HYPERSURFACES COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Schoen, R., Simon, L. 1981; 34 (6): 741-797

    View details for Web of Science ID A1981MQ10300002

  • THE ENERGY AND THE LINEAR MOMENTUM OF SPACE-TIMES IN GENERAL-RELATIVITY COMMUNICATIONS IN MATHEMATICAL PHYSICS Schoen, R., Yau, S. T. 1981; 79 (1): 47-51

    View details for Web of Science ID A1981LG80900005

  • Geometric bounds on the low eigenvalues of a compact surface Proc Symp Pure Math Schoen, R. M., Wolpert, S., Yau, S. T. 1980: 279–285
  • THE STRUCTURE OF COMPLETE STABLE MINIMAL-SURFACES IN 3-MANIFOLDS OF NONNEGATIVE SCALAR CURVATURE COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS FISCHERCOLBRIE, D., Schoen, R. 1980; 33 (2): 199-211

    View details for Web of Science ID A1980JL95500005

  • POSITIVITY OF THE TOTAL MASS OF A GENERAL SPACE-TIME PHYSICAL REVIEW LETTERS Schoen, R., Yau, S. T. 1979; 43 (20): 1457-1459

    View details for Web of Science ID A1979HT23600002

  • PROOF OF THE POSITIVE MASS CONJECTURE IN GENERAL-RELATIVITY COMMUNICATIONS IN MATHEMATICAL PHYSICS Schoen, R., Yau, S. T. 1979; 65 (1): 45-76

    View details for Web of Science ID A1979GN16200003

  • EXISTENCE OF INCOMPRESSIBLE MINIMAL SURFACES AND THE TOPOLOGY OF THREE DIMENSIONAL MANIFOLDS WITH NONNEGATIVE SCALAR CURVATURE ANNALS OF MATHEMATICS Schoen, R., Yau, S. T. 1979; 110 (1): 127-142

    View details for Web of Science ID A1979HM49900004

  • COMPACT GROUP ACTIONS AND THE TOPOLOGY OF MANIFOLDS WITH NON-POSITIVE CURVATURE TOPOLOGY Schoen, R., Yau, S. T. 1979; 18 (4): 361-380

    View details for Web of Science ID A1979HX76600009

  • STRUCTURE OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE MANUSCRIPTA MATHEMATICA Schoen, R., Yau, S. T. 1979; 28 (1-3): 159-183

    View details for Web of Science ID A1979HA99100010

  • PROOF OF THE POSITIVE-ACTION CONJECTURE IN QUANTUM RELATIVITY PHYSICAL REVIEW LETTERS SCHOEN, R. M., Yau, S. T. 1979; 42 (9): 547-548

    View details for Web of Science ID A1979GK08900001

  • UNIVALENT HARMONIC MAPS BETWEEN SURFACES INVENTIONES MATHEMATICAE Schoen, R., Yau, S. T. 1978; 44 (3): 265-278

    View details for Web of Science ID A1978EL94300004

  • INCOMPRESSIBLE MINIMAL SURFACES, 3-DIMENSIONAL MANIFOLDS WITH NONNEGATIVE SCALAR CURVATURE, AND POSITIVE MASS CONJECTURE IN GENERAL RELATIVITY PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Schoen, R., Yau, S. T. 1978; 75 (6): 2567-2567

    Abstract

    We study three-dimensional Riemannian manifolds with nonnegative scalar curvature. We find new topological obstruction for such manifolds. Our method turns out to be useful in studying the positive mass conjecture in general relativity.

    View details for Web of Science ID A1978FF05900007

    View details for PubMedID 16592534

  • REGULARITY AND SINGULARITY ESTIMATES ON HYPERSURFACES MINIMIZING PARAMETRIC ELLIPTIC VARIATIONAL INTEGRALS ACTA MATHEMATICA Schoen, R., Simon, L., ALMGREN, F. J. 1977; 139 (3-4): 217-265

    View details for Web of Science ID A1977EM04500003

  • HARMONIC MAPS AND TOPOLOGY OF STABLE HYPERSURFACES AND MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE COMMENTARII MATHEMATICI HELVETICI Schoen, R., Yau, S. T. 1976; 51 (3): 333-341

    View details for Web of Science ID A1976CR58700004

  • CURVATURE ESTIMATES FOR MINIMAL HYPERSURFACES ACTA MATHEMATICA Schoen, R., Simon, L., Yau, S. T. 1975; 134 (3-4): 275-288

    View details for Web of Science ID A1975AV92500004