Nationality American Role Mathematician Name Richard Schoen | Known for Schoen–Yau conjecture Fields Mathematics | |

Born October 23, 1950 (age 73) Celina, Ohio ( 1950-10-23 ) Institutions Stanford UniversityUniversity of California, BerkeleyUniversity of California, Irvine Notable awards Bocher Memorial Prize (1989) Books Lectures on Differential Geometry, New Energy Technologies for Buildings: Institutional Problems and Solutions Awards MacArthur Fellowship, Guggenheim Fellowship for Natural Sciences, US & Canada, Bocher Memorial Prize Doctoral students Hubert Bray, Jose F. Escobar, William Minicozzi II |

## Jdg 2017 richard schoen the einstein constraint equations

**Richard Melvin Schoen** (born October 23, 1950) is an American mathematician. 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.

## Contents

- Jdg 2017 richard schoen the einstein constraint equations
- 20 11 2015 richard schoen localizing solutions of the einstein equations
- Contributions
- Awards and honors
- Selected publications
- References

## 20 11 2015 richard schoen localizing solutions of the einstein equations

## Contributions

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.

## Selected publications

*Acta Mathematica*,

**134**(3-4): 275–288, MR 423263, doi:10.1007/bf02392104

*Communications in Mathematical Physics*,

**65**(1): 45–76, Bibcode:1979CMaPh..65...45S, MR 526976, doi:10.1007/bf01940959

*Communications on Pure and Applied Mathematics*,

**33**(2): 199–211, MR 562550, doi:10.1002/cpa.3160330206

*Communications in Mathematical Physics*,

**79**(2): 231–260, Bibcode:1981CMaPh..79..231S, MR 612249, doi:10.1007/bf01942062

*Journal of Differential Geometry*,

**17**(2): 307–335, MR 664498

*Journal of Differential Geometry*,

**20**(2): 479–495, MR 788292

*Institut des Hautes Études Scientifiques. Publications Mathématiques*,

**76**: 165–246, MR 1215595, doi:10.1007/bf02699433

*Journal of Differential Geometry*,

**58**(1): 1–86, MR 1895348

*Journal of the AMS*,

**22**(1): 287–307, Bibcode:2009JAMS...22..287B, MR 2449060, doi:10.1090/s0894-0347-08-00613-9