Richard Schoen
Richard Melvin Schoen (born October 23, 1950) is an American mathematician known for his work in differential geometry.
Richard Schoen  

Richard Schoen in 1976 (photo by George Bergman)  
Born  
Nationality  American 
Alma mater  Stanford University 
Known for  
Awards 

Scientific career  
Fields  Mathematics 
Institutions  Stanford University University of California, Berkeley University of California, Irvine 
Doctoral advisor  
Doctoral students 
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, ShingTung 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.
His students include Hubert Bray, José F. Escobar, Ailana Fraser, Chikako Mese, William Minicozzi, and André Neves.[4].
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.[5] In 2015, he was elected Vice President of the American Mathematical Society.[6] He received the Wolf Prize in Mathematics for 2017, shared with Charles Fefferman.[7]. In the same year, he was awarded the Lobachevsky Medal and Prize by Kazan Federal University. [8]
Selected publications
 Schoen, Richard M.; Simon, Leon; Yau, ShingTung (1975), "Curvature estimates for minimal hypersurfaces", Acta Mathematica, 134 (3–4): 275–288, doi:10.1007/bf02392104, MR 0423263
 Schoen, Richard M.; Yau, ShingTung (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
 FischerColbrie, Doris; Schoen, Richard M. (1980), "The structure of complete stable minimal surfaces in 3manifolds 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, ShingTung (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 padic 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, arXiv:math/0008244, MR 1895348
 Brendle, Simon; Schoen, Richard M. (2009), "Manifolds with 1/4pinched curvature are space forms", Journal of the AMS, 22 (1): 287–307, arXiv:0705.0766, Bibcode:2009JAMS...22..287B, doi:10.1090/s0894034708006139, MR 2449060
References
 "Richard Melvin Schoen". School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved 6 January 2017.
 "Richard Schoen Announced as the Winner of the 2017 Lobachevsky Medal and Prize".
 http://www.rolfschockprizes.se/download/18.39ee338a159fb6d5d78e05/1489565086195/pop_matematik_en_170314_FINAL.pdf
 "Richard Schoen  The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 20190312.
 List of Fellows of the American Mathematical Society, retrieved 20130714.
 "American Mathematical Society". Retrieved 25 May 2016.
 The Wolf Foundation – "Richard Schoen Winner of Wolf Prize in Mathematics  2017"
 Lobachevsky Medal and Prize Awarded to Richard Schoen
External links
 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.