Richard Schoen


Richard Melvin Schoen is an American mathematician known for his work in differential geometry.
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 is a 1983 MacArthur Fellow.

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 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.
His students include Hubert Bray, José F. Escobar, Ailana Fraser, Chikako Mese, William Minicozzi, and André Neves.

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. In the same year, he was awarded the Lobachevsky Medal and Prize by Kazan Federal University.

Selected publications