#7,452

Most Influential Person

American mathematician

According to Wikipedia, Richard Melvin Schoen is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984. Career 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. After faculty positions at the Courant Institute, NYU, University of California, Berkeley, and University of California, San Diego, he was Professor at Stanford University from 1987-2014, as Bass Professor of Humanities and Sciences since 1992. He is currently Distinguished Professor and Excellence in Teaching Chair at the University of California, Irvine. His surname is pronounced "Shane."

- Lectures on Differential Geometry (1994) (1310)
- On the proof of the positive mass conjecture in general relativity (1979) (1100)
- Conformal deformation of a Riemannian metric to constant scalar curvature (1984) (1065)
- Proof of the positive mass theorem. II (1981) (660)
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature (1980) (601)
- Existence of incompressible minimal surfaces and the topology of three - dimensional manifolds with (1979) (536)
- On the structure of manifolds with positive scalar curvature (1979) (512)
- Variational theory for the total scalar curvature functional for riemannian metrics and related topics (1989) (497)
- A regularity theory for harmonic maps (1982) (486)
- Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one (1992) (441)
- Sobolev spaces and harmonic maps for metric space targets (1993) (425)
- Conformally flat manifolds, Kleinian groups and scalar curvature (1988) (420)
- Boundary regularity and the Dirichlet problem for harmonic maps (1983) (404)
- Uniqueness, symmetry, and embeddedness of minimal surfaces (1983) (374)
- Analytic Aspects of the Harmonic Map Problem (1984) (314)
- Curvature estimates for minimal hypersurfaces (1975) (310)
- Manifolds with 1/4-pinched curvature are space forms (2007) (294)
- Lp and mean value properties of subharmonic functions on Riemannian manifolds (1984) (251)
- Regularity of stable minimal hypersurfaces (1981) (248)
- Estimates for stable minimal surfaces in three dimensional manifolds (1984) (248)
- Positive harmonic functions on complete manifolds of negative curvature (1985) (244)
- On the Asymptotics for the Vacuum Einstein Constraint Equations (2003) (235)
- A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions (2005) (234)
- Prescribed scalar curvature on then-sphere (1996) (217)
- The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation (1988) (212)
- On univalent harmonic maps between surfaces (1978) (206)
- The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature (1985) (199)
- The first Steklov eigenvalue, conformal geometry, and minimal surfaces (2009) (195)
- Sharp eigenvalue bounds and minimal surfaces in the ball (2012) (180)
- Conformal metrics with prescribed scalar curvature (1986) (173)
- Refined asymptotics for constant scalar curvature metrics with isolated singularities (1998) (164)
- The existence of a black hole due to condensation of matter (1983) (163)
- A Compactness Theorem for the Yamabe Problem (2009) (157)
- Lectures on Harmonic Maps (1997) (156)
- Positivity of the Total Mass of a General Space-Time (1979) (141)
- Minimizing area among Lagrangian surfaces: The mapping problem (2000) (137)
- Positive scalar curvature and minimal hypersurface singularities (2017) (132)
- Global existence theorems for harmonic maps to non-locally compact spaces (1997) (130)
- Classification of manifolds with weakly 1/4-pinched curvatures (2007) (126)
- Compact group actions and the topology of manifolds with non-positive curvature (1979) (125)
- Regularity of minimizing harmonic maps into the sphere (1984) (124)
- COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE (1982) (110)
- The energy and the linear momentum of space-times in general relativity (1981) (104)
- Proof of the Positive-Action Conjecture in Quantum Relativity (1979) (99)
- On the conformal and CR automorphism groups (1995) (83)
- Proof That the Bondi Mass is Positive (1982) (77)
- Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals (1977) (72)
- KIDs are Non-Generic (2004) (72)
- The spacetime positive mass theorem in dimensions less than eight (2011) (62)
- Localizing solutions of the Einstein constraint equations (2014) (62)
- On the Gauss map of complete surfaces of constant mean curvature in R3 and R4 (1982) (61)
- GEOMETRIC BOUNDS ON THE LOW EIGENVALUES OF A COMPACT SURFACE (1980) (54)
- On the existence of harmonic diffeomorphisms between surfaces (1982) (54)
- Uniqueness theorems for free boundary minimal disks in space forms (2014) (53)
- On the Bartnik mass of apparent horizons (2014) (53)
- Minimal surfaces and eigenvalue problems (2013) (50)
- Minimizing volume among Lagrangian submanifolds (1999) (46)
- A report on some recent progress on non-linear problems in geometry (1990) (43)
- Complete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity. (1979) (38)
- On the isoperimetric inequality for minimal surfaces (1984) (37)
- Handbook of Geometric Analysis (2010) (34)
- A lower bound for the first eigenvalue of a negatively curved manifold (1982) (34)
- Convexity of Reduced Energy and Mass Angular Momentum Inequalities (2012) (31)
- Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity. (1978) (31)
- Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets (2010) (29)
- Sphere Theorems in Geometry (2009) (27)
- BLOW-UP PHENOMENA FOR THE YAMABE EQUATION (2008) (27)
- Curvature, sphere theorems, and the Ricci flow (2010) (27)
- Shape optimization for the Steklov problem in higher dimensions (2017) (26)
- REGULARITY OF SIMPLY CONNECTED SURFACES WITH QUASICONFORMAL GAUSS MAP (1984) (26)
- Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space (2006) (22)
- On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds (2009) (22)
- On static n-body configurations in relativity (2008) (19)
- The effect of curvature on the behavior of harmonic functions and mappings (1995) (18)
- Theorems of Barth-Lefschetz type and Morse theory on the space of paths (1998) (18)
- The Structure of Manifolds with Positive Scalar Curvature (1987) (16)
- Correction to: ``A regularity theory for harmonic maps'' (1983) (16)
- Existence and regularity theorems for some geometric variational problems (1977) (15)
- The Volume Functional for Lagrangian Submanifolds (2002) (14)
- Some results on higher eigenvalue optimization (2019) (14)
- Recent Proofs of the Riemannian Penrose Conjecture (1999) (12)
- Initial data and the Einstein constraint equations (2015) (8)
- Gravitating opposites attract (2009) (8)
- Complete manifolds with bounded curvature and spectral gaps (2015) (6)
- Riemannian Manifolds of Positive Curvature (2011) (6)
- Selected expository works of Shing-Tung Yau with commentary (2014) (6)
- Existence and geometric structure of metrics on surfaces which extremize eigenvalues (2013) (5)
- Geometry and global analysis : report of the First MSJ International Research Institute, July 12-23, 1993, Tohoku University, Sendai, Japan (1993) (4)
- MEAN CURVATURE FLOW AND LAGRANGIAN EMBEDDINGS (2003) (3)
- Regularity and evolution of nonlinear equations : essays dedicated to Richard Hamilton, Leon Simon, and Karen Uhlenbeck (2015) (3)
- On the Bartnik mass of outermost apparent horizons (2014) (3)
- MANIFOLDS WITH POINTWISE 1/4-PINCHED CURVATURE (2007) (3)
- SOME COMPACTNESS RESULTS RELATED TO SCALAR CURVATURE DEFORMATION (2006) (2)
- Minimal Submanifolds of Higher Codimension (2018) (2)
- A remark on minimal hypercones. (1982) (2)
- New developments in the theory of geometric partial differential equations (1986) (2)
- Topics in Scalar Curvature Spring 2017 (2017) (1)
- Corrections to “compact group actions and the topology of manifolds with non-positive curvature” (1982) (1)
- Lectures on geometric variational problems (1996) (1)
- The theory and applications of harmonic mappings between riemannian manifolds (1992) (1)
- Eigenvalues and general relativity (2019) (0)
- Selected Works of Shing-Tung Yau (2019) (0)
- A Review of Geometric Variational Problems (1996) (0)
- Symmetry Considerations, Topological Constraints, and Interactions with Physics (1996) (0)
- Reductive group actions with one-dimensional quotient . Sur les espaces homogènes modèles de variétés compactes . Affine quivers and canonical bases . Harmonic maps into singular spaces and p-adic superrigidity for lattices in groups of rank one (1992) (0)
- 0 40 30 42 v 1 1 0 M ar 2 00 4 KIDs are non-generic (2008) (0)
- Metric Geometry and Harmonic Functions (2019) (0)
- ON A FREE BOUNDARY PROBLEM FOR EMBEDDED MINIMAL SURFACES AND INSTABILITY THEOREMS FOR MANIFOLDS WITH POSITIVE ISOTROPIC CURVATURE (2011) (0)
- Marsden Memorial Lecture: The constraint manifold of general relativity (2016) (0)
- Report on Workshop 03w5074: Perspectives in Differential Geometry (0)
- Area estimates and rigidity of capillary H−surfaces in three-manifolds with boundary (2015) (0)
- BERNSTEIN THEOREMS FOR LENGTH AND AREA DECREASING MINIMAL MAPS (2013) (0)
- Geometric analysis and related topics (2017) (0)
- The General Setting (1996) (0)
- Metric Geometry and Minimal Submanifolds (2019) (0)
- Geometric Analysis and Spectral Theory Aisenstadt Chairs (2012) (0)

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