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(photo by George Bergman)
October 23, 1950 |
University of California, Berkeley
University of California, Irvine
|Alma mater||Stanford University|
|Doctoral advisor||Leon Simon
|Doctoral students||Hubert Bray
José F. Escobar
|Known for||Differentiable sphere theorem
Solution of positive mass conjecture
|Notable awards||Bôcher Memorial Prize (1989)|
Richard Melvin Schoen (born October 23, 1950) is an American mathematician. Born in Fort Recovery, Ohio, he received his PhD in 1977 from Stanford University. Schoen is currently an Excellence in Teaching Chair at the University of California, Irvine. His surname is pronounced "Shane," perhaps as a reflection of the regional dialect spoken by some of his German ancestors.
Schoen has investigated the use of analytic techniques in global differential geometry. In 1979, together with his former doctoral supervisor, Shing-Tung Yau, he proved the fundamental positive energy theorem in general relativity. In 1983, he was awarded a MacArthur Fellowship, and in 1984, he obtained a complete solution to the Yamabe problem on compact manifolds. This work combined new techniques with ideas developed in earlier work with Yau, and partial results by Thierry Aubin and Neil Trudinger. The resulting theorem asserts that any Riemannian metric on a closed manifold may be conformally rescaled (that is, multiplied by a suitable positive function) so as to produce a metric of constant scalar curvature. In 2007, Simon Brendle and Richard Schoen proved the differentiable sphere theorem, a fundamental result in the study of manifolds of positive sectional curvature. He has also made fundamental contributions to the regularity theory of minimal surfaces and harmonic maps.
Awards and honors
For his work on the Yamabe problem, Schoen was awarded the Bôcher Memorial Prize in 1989. He joined the American Academy of Arts and Sciences in 1988 and the National Academy of Sciences in 1991, and won a Guggenheim Fellowship in 1996. In 2012 he became a fellow of the American Mathematical Society. In 2015, he was elected Vice President of the American Mathematical Society.
- Schoen, Richard M.; Simon, Leon; Yau, Shing-Tung (1975), "Curvature estimates for minimal hypersurfaces", Acta Mathematica 134 (3-4): 275–288, doi:10.1007/bf02392104, MR 423263
- Schoen, Richard M.; Yau, Shing-Tung (1979), "On the proof of the positive mass conjecture in general relativity", Communications in Mathematical Physics 65 (1): 45–76, Bibcode:1979CMaPh..65...45S, doi:10.1007/bf01940959, MR 526976
- Fischer-Colbrie, Doris; Schoen, Richard M. (1980), "The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature", Communications on Pure and Applied Mathematics 33 (2): 199–211, doi:10.1002/cpa.3160330206, MR 562550
- Schoen, Richard M.; Yau, Shing-Tung (1981), "Proof of the positive mass theorem. II", Communications in Mathematical Physics 79 (2): 231–260, Bibcode:1981CMaPh..79..231S, doi:10.1007/bf01942062, MR 612249
- Schoen, Richard M.; Uhlenbeck, Karen (1982), "A regularity theory for harmonic maps", Journal of Differential Geometry 17 (2): 307–335, MR 664498
- Schoen, Richard M. (1984), "Conformal deformation of a Riemannian metric to constant scalar curvature", Journal of Differential Geometry 20 (2): 479–495, MR 788292
- Gromov, Mikhael; Schoen, Richard M. (1992), "Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one", Institut des Hautes Études Scientifiques. Publications Mathématiques 76: 165–246, doi:10.1007/bf02699433, MR 1215595
- Schoen, Richard M.; Wolfson, Jon (2001), "Minimizing area among Lagrangian surfaces: the mapping problem", Journal of Differential Geometry 58 (1): 1–86, MR 1895348
- Brendle, Simon; Schoen, Richard M. (2009), "Manifolds with 1/4-pinched curvature are space forms", Journal of the AMS 22 (1): 287–307, Bibcode:2009JAMS...22..287B, doi:10.1090/s0894-0347-08-00613-9, MR 2449060
- List of Fellows of the American Mathematical Society, retrieved 2013-07-14.
- "American Mathematical Society". American Mathematical Society. Retrieved 25 May 2016.