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


  • 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)

2017-18 Courses


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
  • Convexity of Reduced Energy and Mass Angular Momentum Inequalities ANNALES HENRI POINCARE Schoen, R., Zhou, X. 2013; 14 (7): 1747-1773
  • 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
  • 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
  • The first Steklov eigenvalue, conformal geometry, and minimal surfaces ADVANCES IN MATHEMATICS Fraser, A., Schoen, R. 2011; 226 (5): 4011-4030
  • CURVATURE, SPHERE THEOREMS, AND THE RICCI FLOW BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Brendle, S., Schoen, R. 2011; 48 (1): 1-32
  • 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)
  • Manifolds with 1/4-pinched curvature are space forms JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Brendle, S., Schoen, R. 2009; 22 (1): 287-307
  • 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
  • Classification of manifolds with weakly 1/4-pinched curvatures ACTA MATHEMATICA Brendle, S., Schoen, R. M. 2008; 200 (1): 1-13
  • 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
  • On the asymptotics for the vacuum Einstein constraint equations JOURNAL OF DIFFERENTIAL GEOMETRY Corvino, J., Schoen, R. M. 2006; 73 (2): 185-217
  • The mathematics of general relativity: Problems and progress Sesquicentennial Conference of Mathematics at Washington University Schoen, R. AMER MATHEMATICAL SOC. 2006: 119–132
  • 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
  • KIDs are non-generic ANNALES HENRI POINCARE Beig, R., Chrusciel, P. T., Schoen, R. 2005; 6 (1): 155-194
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • CONFORMALLY FLAT MANIFOLDS, KLEINIAN-GROUPS AND SCALAR CURVATURE INVENTIONES MATHEMATICAE Schoen, R., Yau, S. T. 1988; 92 (1): 47-71
  • 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
  • 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
  • REGULARITY OF MINIMIZING HARMONIC MAPS INTO THE SPHERE INVENTIONES MATHEMATICAE Schoen, R., Uhlenbeck, K. 1984; 78 (1): 89-100
  • 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
  • CONFORMAL DEFORMATION OF A RIEMANNIAN METRIC TO CONSTANT SCALAR CURVATURE JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R. 1984; 20 (2): 479-495
  • REGULARITY OF SIMPLY CONNECTED SURFACES WITH QUASICONFORMAL GAUSS MAP ANNALS OF MATHEMATICS STUDIES Schoen, R., Simon, L. 1983: 127-145
  • BOUNDARY-REGULARITY AND THE DIRICHLET PROBLEM FOR HARMONIC MAPS JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R., Uhlenbeck, K. 1983; 18 (2): 253-268
  • UNIQUENESS, SYMMETRY, AND EMBEDDEDNESS OF MINIMAL-SURFACES JOURNAL OF DIFFERENTIAL GEOMETRY SCHOEN, R. M. 1983; 18 (4): 791-809
  • 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
  • ESTIMATES FOR STABLE MINIMAL-SURFACES IN 3 DIMENSIONAL MANIFOLDS ANNALS OF MATHEMATICS STUDIES Schoen, R. 1983: 111-126
  • 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
  • COMPLETE 3 DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE ANNALS OF MATHEMATICS STUDIES Schoen, R., Yau, S. T. 1982: 209-228
  • A REGULARITY THEORY FOR HARMONIC MAPS JOURNAL OF DIFFERENTIAL GEOMETRY Schoen, R., Uhlenbeck, K. 1982; 17 (2): 307-335
  • 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
  • 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
  • ON THE EXISTENCE OF HARMONIC DIFFEOMORPHISMS BETWEEN SURFACES INVENTIONES MATHEMATICAE Jost, J., Schoen, R. 1982; 66 (2): 353-359
  • PROOF OF THE POSITIVE MASS THEOREM .2. COMMUNICATIONS IN MATHEMATICAL PHYSICS Schoen, R., Yau, S. T. 1981; 79 (2): 231-260
  • REGULARITY OF STABLE MINIMAL HYPERSURFACES COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS Schoen, R., Simon, L. 1981; 34 (6): 741-797
  • 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
  • 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
  • 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
  • PROOF OF THE POSITIVE MASS CONJECTURE IN GENERAL-RELATIVITY COMMUNICATIONS IN MATHEMATICAL PHYSICS Schoen, R., Yau, S. T. 1979; 65 (1): 45-76
  • COMPACT GROUP ACTIONS AND THE TOPOLOGY OF MANIFOLDS WITH NON-POSITIVE CURVATURE TOPOLOGY Schoen, R., Yau, S. T. 1979; 18 (4): 361-380
  • STRUCTURE OF MANIFOLDS WITH POSITIVE SCALAR CURVATURE MANUSCRIPTA MATHEMATICA Schoen, R., Yau, S. T. 1979; 28 (1-3): 159-183
  • PROOF OF THE POSITIVE-ACTION CONJECTURE IN QUANTUM RELATIVITY PHYSICAL REVIEW LETTERS SCHOEN, R. M., Yau, S. T. 1979; 42 (9): 547-548
  • POSITIVITY OF THE TOTAL MASS OF A GENERAL SPACE-TIME PHYSICAL REVIEW LETTERS Schoen, R., Yau, S. T. 1979; 43 (20): 1457-1459
  • UNIVALENT HARMONIC MAPS BETWEEN SURFACES INVENTIONES MATHEMATICAE Schoen, R., Yau, S. T. 1978; 44 (3): 265-278
  • 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
  • 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
  • CURVATURE ESTIMATES FOR MINIMAL HYPERSURFACES ACTA MATHEMATICA Schoen, R., Simon, L., Yau, S. T. 1975; 134 (3-4): 275-288