Richard Schoen
Encyclopedia
Richard Melvin Schoen is an American
mathematician
. Born in Fort Recovery
, Ohio, he received his PhD in 1977 from Stanford University
where he is currently the Anne T. and Robert M. Bass Professor of Humanities and Sciences. His surname is pronounced "Shane," perhaps as a reflection of the regional dialect spoken by some of his German
ancestor
s.
Schoen is a world expert in 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
. 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 2007, Simon Brendle and Richard Schoen proved the differentiable sphere theorem, a fundamental result in the study of manifolds of positive sectional curvature
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Born in Fort Recovery
Fort Recovery
Fort Recovery was a United States Army fort begun in late 1793 and completed in March 1794 under orders by General "Mad" Anthony Wayne. It was located on the site of the present-day village of Fort Recovery, Ohio, United States, on the Wabash River within two miles of the boundary with...
, Ohio, he received his PhD in 1977 from Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
where he is currently the Anne T. and Robert M. Bass Professor of Humanities and Sciences. His surname is pronounced "Shane," perhaps as a reflection of the regional dialect spoken by some of his German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
ancestor
Ancestor
An ancestor is a parent or the parent of an ancestor ....
s.
Schoen is a world expert in the use of analytic techniques in global differential geometry.
In 1979, together with his former doctoral supervisor, Shing-Tung Yau
Shing-Tung Yau
Shing-Tung Yau is a Chinese American mathematician working in differential geometry. He was born in Shantou, Guangdong Province, China into a family of scholars from Jiaoling, Guangdong Province....
, he proved the fundamental positive energy theorem
Positive energy theorem
In general relativity, the positive energy theorem states that, assuming the dominant energy condition, the mass of an asymptotically flat spacetime is non-negative; furthermore, the mass is zero only for Minkowski spacetime...
in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. In 1983, he was awarded a MacArthur Fellowship
MacArthur Fellows Program
The MacArthur Fellows Program or MacArthur Fellowship is an award given by the John D. and Catherine T...
,
and in 1984, he obtained a complete solution to the Yamabe problem
Yamabe problem
The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, and takes its name from the mathematician Hidehiko Yamabe. Although claimed to have a solution in 1960, a critical error...
on compact manifolds.
This work combined new techniques with ideas developed in earlier work with Yau, and partial results by
Thierry Aubin
Thierry Aubin
Thierry Aubin was a French mathematician at Centre de Mathématiques de Jussieu who worked on Riemannian geometryand non-linear partial differential equations...
and Neil Trudinger
Neil Trudinger
Neil Sidney Trudinger is an Australian mathematician, known particularly for his work in the field of nonlinear elliptic partial differential equations....
. The resulting theorem asserts that
any Riemannian metric on a closed manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
may be conformally rescaled (that is, multiplied by a suitable
positive function) so as to produce a metric of constant scalar curvature
Scalar curvature
In Riemannian geometry, the scalar curvature is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the manifold near that point...
. For his work on the Yamabe problem, Schoen was awarded the Bôcher Memorial Prize
Bôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 . It is awarded every five years for a notable research memoir in analysis that has appeared during the past six years in a recognized North American...
in 1989. He joined the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 1988 and the National Academy of Sciences
United States National Academy of Sciences
The National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
in 1991, and won a Guggenheim Fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
in 1996. In 2007, Simon Brendle and Richard Schoen proved the differentiable sphere theorem, a fundamental result in the study of manifolds of positive sectional curvature
Sectional curvature
In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds. The sectional curvature K depends on a two-dimensional plane σp in the tangent space at p...
.