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Richard Schoen in 1976
(photo by George Bergman)
|Alma mater||Stanford University|
|Known for||Differentiable sphere theorem|
Solution of positive mass conjecture
|Awards||Bôcher Memorial Prize (1989)|
Wolf Prize (2017)
Heinz Hopf Prize (2017)
Lobachevsky Prize (2017)
Rolf Schock Prize (2017)
University of California, Berkeley
University of California, Irvine
|Doctoral advisor||Leon Simon|
|Doctoral students||Hubert Bray|
José F. Escobar
Born in Celina, Ohio, and a 1968 graduate of Fort Recovery High School, he received his B.S. from the University of Dayton in mathematics. He then received his PhD in 1977 from Stanford University and 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. He received the Wolf Prize in Mathematics for 2017, shared with Charles Fefferman.
- 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 0423263
- 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 0526976
- 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 0562550
- 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 0612249
- Schoen, Richard M.; Uhlenbeck, Karen (1982), "A regularity theory for harmonic maps", Journal of Differential Geometry, 17 (2): 307–335, MR 0664498
- Schoen, Richard M. (1984), "Conformal deformation of a Riemannian metric to constant scalar curvature", Journal of Differential Geometry, 20 (2): 479–495, MR 0788292
- 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, arXiv:0705.0766, Bibcode:2009JAMS...22..287B, doi:10.1090/s0894-0347-08-00613-9, MR 2449060
- "Richard Melvin Schoen". School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved 6 January 2017.
- List of Fellows of the American Mathematical Society, retrieved 2013-07-14.
- "American Mathematical Society". American Mathematical Society. Retrieved 25 May 2016.
- The Wolf Foundation – "Richard Schoen Winner of Wolf Prize in Mathematics - 2017"
- Personal web site
- O'Connor, John J.; Robertson, Edmund F., "Richard Schoen", MacTutor History of Mathematics archive, University of St Andrews.
- Richard Schoen at the Mathematics Genealogy Project
- Sormani, Christina (August 2018). "The Mathematics of Richard Schoen" (PDF). Notices of the American Mathematical Society. 65 (11): 1349–1376.