# Richard Schoen

American mathematician

## Richard Schoen's AcademicInfluence.com Rankings

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Mathematics

## Richard Schoen's Degrees

- PhD Mathematics Stanford University
- Bachelors Mathematics University of California, Berkeley

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## Why Is Richard Schoen Influential?

(Suggest an Edit or Addition)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."

## Richard Schoen's Published Works

### Published Works

- Lectures on Differential Geometry (1994) (1564)
- On the proof of the positive mass conjecture in general relativity (1979) (1233)
- Conformal deformation of a Riemannian metric to constant scalar curvature (1984) (1158)
- Proof of the positive mass theorem. II (1981) (693)
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature (1980) (657)
- On the structure of manifolds with positive scalar curvature (1979) (571)
- Existence of incompressible minimal surfaces and the topology of three - dimensional manifolds with (1979) (555)
- Variational theory for the total scalar curvature functional for riemannian metrics and related topics (1989) (552)
- Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one (1992) (475)
- Conformally flat manifolds, Kleinian groups and scalar curvature (1988) (471)
- Sobolev spaces and harmonic maps for metric space targets (1993) (457)
- A regularity theory for harmonic maps (1982) (453)
- Boundary regularity and the Dirichlet problem for harmonic maps (1983) (444)
- Uniqueness, symmetry, and embeddedness of minimal surfaces (1983) (399)
- Curvature estimates for minimal hypersurfaces (1975) (344)
- Manifolds with 1/4-pinched curvature are space forms (2007) (338)
- Analytic Aspects of the Harmonic Map Problem (1984) (334)
- Regularity of stable minimal hypersurfaces (1981) (289)
- Lp and mean value properties of subharmonic functions on Riemannian manifolds (1984) (279)
- On the Asymptotics for the Vacuum Einstein Constraint Equations (2003) (264)
- Positive harmonic functions on complete manifolds of negative curvature (1985) (263)
- Estimates for stable minimal surfaces in three dimensional manifolds (1984) (262)
- A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions (2005) (257)
- The first Steklov eigenvalue, conformal geometry, and minimal surfaces (2009) (243)
- Prescribed scalar curvature on then-sphere (1996) (233)
- The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation (1988) (232)
- Sharp eigenvalue bounds and minimal surfaces in the ball (2012) (225)
- On univalent harmonic maps between surfaces (1978) (220)
- The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature (1985) (213)
- Conformal metrics with prescribed scalar curvature (1986) (193)
- Refined asymptotics for constant scalar curvature metrics with isolated singularities (1998) (183)
- A Compactness Theorem for the Yamabe Problem (2009) (177)
- The existence of a black hole due to condensation of matter (1983) (174)
- Positive scalar curvature and minimal hypersurface singularities (2017) (157)
- Positivity of the Total Mass of a General Space-Time (1979) (147)
- Minimizing area among Lagrangian surfaces: The mapping problem (2000) (146)
- Classification of manifolds with weakly 1/4-pinched curvatures (2007) (141)
- Regularity of minimizing harmonic maps into the sphere (1984) (134)
- Compact group actions and the topology of manifolds with non-positive curvature (1979) (133)
- Global existence theorems for harmonic maps to non-locally compact spaces (1997) (133)
- Lectures on Harmonic Maps (1997) (121)
- COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE (1982) (119)
- The energy and the linear momentum of space-times in general relativity (1981) (113)
- Proof of the Positive-Action Conjecture in Quantum Relativity (1979) (102)
- On the conformal and CR automorphism groups (1995) (92)
- KIDs are Non-Generic (2004) (83)
- Proof That the Bondi Mass is Positive (1982) (81)
- The spacetime positive mass theorem in dimensions less than eight (2011) (80)
- Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals (1977) (76)
- Localizing solutions of the Einstein constraint equations (2014) (75)
- Uniqueness theorems for free boundary minimal disks in space forms (2014) (72)
- Minimal surfaces and eigenvalue problems (2013) (65)
- On the Bartnik mass of apparent horizons (2014) (64)
- On the Gauss map of complete surfaces of constant mean curvature in R3 and R4 (1982) (64)
- GEOMETRIC BOUNDS ON THE LOW EIGENVALUES OF A COMPACT SURFACE (1980) (58)
- On the existence of harmonic diffeomorphisms between surfaces (1982) (56)
- Minimizing volume among Lagrangian submanifolds (1999) (50)
- A report on some recent progress on non-linear problems in geometry (1990) (46)
- Complete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity. (1979) (45)
- Handbook of Geometric Analysis (2010) (42)
- On the isoperimetric inequality for minimal surfaces (1984) (41)
- Convexity of Reduced Energy and Mass Angular Momentum Inequalities (2012) (40)
- Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets (2010) (38)
- Sphere Theorems in Geometry (2009) (35)
- A lower bound for the first eigenvalue of a negatively curved manifold (1982) (35)
- Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity. (1978) (33)
- Curvature, sphere theorems, and the Ricci flow (2010) (32)
- On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds (2009) (29)
- Shape optimization for the Steklov problem in higher dimensions (2017) (27)
- REGULARITY OF SIMPLY CONNECTED SURFACES WITH QUASICONFORMAL GAUSS MAP (1984) (26)
- Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space (2006) (23)
- Theorems of Barth-Lefschetz type and Morse theory on the space of paths (1998) (21)
- On static n-body configurations in relativity (2008) (21)
- The effect of curvature on the behavior of harmonic functions and mappings (1995) (19)
- Some results on higher eigenvalue optimization (2019) (18)
- The Structure of Manifolds with Positive Scalar Curvature (1987) (16)
- Correction to: ``A regularity theory for harmonic maps'' (1983) (16)
- The Volume Functional for Lagrangian Submanifolds (2002) (16)
- Recent Proofs of the Riemannian Penrose Conjecture (1999) (14)
- BLOW-UP PHENOMENA FOR THE YAMABE EQUATION (2008) (14)
- Existence and regularity theorems for some geometric variational problems (1977) (14)
- Initial data and the Einstein constraint equations (2015) (10)
- Riemannian Manifolds of Positive Curvature (2011) (9)
- Selected expository works of Shing-Tung Yau with commentary (2014) (9)
- Gravitating opposites attract (2009) (8)
- Existence and geometric structure of metrics on surfaces which extremize eigenvalues (2013) (7)
- MEAN CURVATURE FLOW AND LAGRANGIAN EMBEDDINGS (2003) (6)
- Complete manifolds with bounded curvature and spectral gaps (2015) (6)
- Regularity and evolution of nonlinear equations : essays dedicated to Richard Hamilton, Leon Simon, and Karen Uhlenbeck (2015) (5)
- SOME COMPACTNESS RESULTS RELATED TO SCALAR CURVATURE DEFORMATION (2006) (4)
- Geometry and global analysis : report of the First MSJ International Research Institute, July 12-23, 1993, Tohoku University, Sendai, Japan (1993) (4)
- On the Bartnik mass of outermost apparent horizons (2014) (3)
- MANIFOLDS WITH POINTWISE 1/4-PINCHED CURVATURE (2007) (3)
- 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)
- The theory and applications of harmonic mappings between riemannian manifolds (1992) (1)
- Sharp eigenvalue bounds and minimal surfaces in the ball (2015) (1)
- Minimal Submanifolds of Higher Codimension (2018) (1)
- Lectures on geometric variational problems (1996) (1)
- ON A FREE BOUNDARY PROBLEM FOR EMBEDDED MINIMAL SURFACES AND INSTABILITY THEOREMS FOR MANIFOLDS WITH POSITIVE ISOTROPIC CURVATURE (2011) (1)
- Corrections to “compact group actions and the topology of manifolds with non-positive curvature” (1982) (1)
- On the first and second homotopy groups of manifolds with positive curvature (2023) (0)
- Geometric analysis and related topics (2017) (0)
- Metric Geometry and Minimal Submanifolds (2019) (0)
- Existence and geometric structure of metrics on surfaces which extremize eigenvalues (2013) (0)
- BERNSTEIN THEOREMS FOR LENGTH AND AREA DECREASING MINIMAL MAPS (2013) (0)
- Symmetry Considerations, Topological Constraints, and Interactions with Physics (1996) (0)
- Preface to Peter Li Volume (2022) (0)
- Localizing solutions of the Einstein constraint equations (2015) (0)
- Selected Works of Shing-Tung Yau (2019) (0)
- The General Setting (1996) (0)
- Stability and largeness properties of minimal surfaces in higher codimension (2023) (0)
- Metric Geometry and Harmonic Functions (2019) (0)
- Marsden Memorial Lecture: The constraint manifold of general relativity (2016) (0)
- A Review of Geometric Variational Problems (1996) (0)
- Geometric Analysis and Spectral Theory Aisenstadt Chairs (2012) (0)
- 0 40 30 42 v 1 1 0 M ar 2 00 4 KIDs are non-generic (2008) (0)
- Convexity of Reduced Energy and Mass Angular Momentum Inequalities (2013) (0)
- Eigenvalues and general relativity (2019) (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)
- Area estimates and rigidity of capillary H−surfaces in three-manifolds with boundary (2015) (0)
- Report on Workshop 03w5074: Perspectives in Differential Geometry (0)

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