Richard Schoen

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All published works

Action	Title	Year	Authors
+	Stability and largeness properties of minimal surfaces in higher codimension	2023	Ailana Fraser Richard Schoen
+	On the first and second homotopy groups of manifolds with positive curvature	2023	Richard Schoen
+	Partial Differential Equations	2022	Guido De Philippis Richard Schoen Felix Schulze
+ PDF Chat	Some results on higher eigenvalue optimization	2020	Ailana Fraser Richard Schoen
+	Some results on higher eigenvalue optimization	2019	Ailana Fraser Richard Schoen
+ PDF Chat	Shape optimization for the Steklov problem in higher dimensions	2019	Ailana Fraser Richard Schoen
+ PDF Chat	Positive scalar curvature and minimal hypersurface singularities	2019	Richard Schoen Shing‐Tung Yau
+	Selected Works of Shing-Tung Yau	2019	Suyu Cheng Huai-Dong Cao Jun Li Richard Schoen
+	Metric Geometry and Minimal Submanifolds	2019	Shing Tung Yau Huai-Dong Cao Jun Li Richard Schoen
+	Eigenvalues and general relativity	2019	Shing Tung Yau Huai-Dong Cao Jun Li Richard Schoen
+	Metric Geometry and Harmonic Functions	2019	Shing Tung Yau Huai-Dong Cao Jun Li Richard Schoen
+	Some results on higher eigenvalue optimization	2019	Ailana Fraser Richard Schoen
+	Partial Differential Equations	2018	Camillo De Lellis Richard Schoen Peter M. Topping
+	Shape optimization for the Steklov problem in higher dimensions	2017	Ailana Fraser Richard Schoen
+	Positive Scalar Curvature and Minimal Hypersurface Singularities	2017	Richard Schoen Shing‐Tung Yau
+	Shape optimization for the Steklov problem in higher dimensions	2017	Ailana Fraser Richard Schoen
+ PDF Chat	Complete manifolds with bounded curvature and spectral gaps	2016	Richard Schoen Hung Tran
+ PDF Chat	Localizing solutions of the Einstein constraint equations	2015	Alessandro Carlotto Richard Schoen
+ PDF Chat	The spacetime positive mass theorem in dimensions less than eight	2015	Michael Eichmair Lan-Hsuan Huang Dan A. Lee Richard Schoen
+	Complete manifolds with bounded curvature and spectral gaps	2015	Richard Schoen Hung Tran
+ PDF Chat	On the Bartnik mass of apparent horizons	2015	Christos Mantoulidis Richard Schoen
+ PDF Chat	Sharp eigenvalue bounds and minimal surfaces in the ball	2015	Ailana Fraser Richard Schoen
+	Complete manifolds with bounded curvature and spectral gaps	2015	Richard Schoen Hung Tran
+	Regularity and evolution of nonlinear equations : essays dedicated to Richard Hamilton, Leon Simon, and Karen Uhlenbeck	2015	Huai-Dong Cao Richard Schoen Shing Tung Yau
+	On the Bartnik mass of outermost apparent horizons	2014	Christos Mantoulidis Richard Schoen
+ PDF Chat	Uniqueness Theorems for Free Boundary Minimal Disks in Space Forms	2014	Ailana Fraser Richard Schoen
+	Uniqueness theorems for free boundary minimal disks in space forms	2014	Ailana Fraser Richard Schoen
+	Localizing solutions of the Einstein constraint equations	2014	Alessandro Carlotto Richard Schoen
+	Uniqueness theorems for free boundary minimal disks in space forms	2014	Ailana Fraser Richard Schoen
+	Localizing solutions of the Einstein constraint equations	2014	Alessandro Carlotto Richard Schoen
+	Existence and geometric structure of metrics on surfaces which extremize eigenvalues	2013	Richard Schoen
+ PDF Chat	Convexity of Reduced Energy and Mass Angular Momentum Inequalities	2013	Richard Schoen Xin Zhou
+ PDF Chat	Minimal surfaces and eigenvalue problems	2013	Ailana Fraser Richard Schoen
+	Minimal surfaces and eigenvalue problems	2013	Ailana Fraser Richard Schoen
+	Eigenvalue bounds and minimal surfaces in the ball	2012	Ailana Fraser Richard Schoen
+	The spacetime positive mass theorem in dimensions less than eight	2011	Michael Eichmair Lan-Hsuan Huang Dan A. Lee Richard Schoen
+ PDF Chat	On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds	2011	Dominic Joyce Yng-Ing Lee Richard Schoen
+ PDF Chat	Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets	2011	Lan-Hsuan Huang Richard Schoen Mu‐Tao Wang
+	Riemannian Manifolds of Positive Curvature	2011	Simon Brendle Richard Schoen
+	The spacetime positive mass theorem in dimensions less than eight	2011	Michael Eichmair Lan-Hsuan Huang Dan A. Lee Richard Schoen
+	The first Steklov eigenvalue, conformal geometry, and minimal surfaces	2010	Ailana Fraser Richard Schoen
+ PDF Chat	Curvature, Sphere Theorems, and the Ricci flow	2010	Simon Brendle Richard Schoen
+	Handbook of Geometric Analysis	2010	Lizhen Ji P. Li Richard Schoen Luciano de Simon
+	Curvature, sphere theorems, and the Ricci flow	2010	Simon Brendle Richard Schoen
+	The first Steklov eigenvalue, conformal geometry, and minimal surfaces	2009	Ailana Fraser Richard Schoen
+ PDF Chat	Gravitating opposites attract	2009	Robert Beig G. W. Gibbons Richard Schoen
+ PDF Chat	On static <i>n</i> -body configurations in relativity	2009	Robert Beig Richard Schoen
+	On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds	2009	Dominic Joyce Yng-Ing Lee Richard Schoen
+ PDF Chat	A compactness theorem for the Yamabe problem	2009	Marcus Khuri Fernando C. Marques Richard Schoen
+	Sphere Theorems in Geometry	2009	Simon Brendle Richard Schoen
+	The first Steklov eigenvalue, conformal geometry, and minimal surfaces	2009	Ailana Fraser Richard Schoen
+	On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds	2009	Dominic Joyce Yng-Ing Lee Richard Schoen
+	Manifolds with 1/4-pinched curvature are space forms	2008	Simon Brendle Richard Schoen
+ PDF Chat	Classification of manifolds with weakly 1/4-pinched curvatures	2008	Simon Brendle Richard Schoen
+ PDF Chat	Sphere theorems in geometry	2008	Simon Brendle Richard Schoen
+	Riemannian Manifolds of Positive Curvature	2007	Richard Schoen
+	Classification of manifolds with weakly 1/4-pinched curvatures	2007	Simon Brendle Richard Schoen
+	Manifolds with 1/4-pinched Curvature are Space Forms	2007	Simon Brendle Richard Schoen
+ PDF Chat	A Generalization of Hawking’s Black Hole Topology Theorem to Higher Dimensions	2006	Gregory J. Galloway Richard Schoen
+ PDF Chat	On the Asymptotics for the Vacuum Einstein Constraint Equations	2006	Justin Corvino Richard Schoen
+	Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space	2006	Bo Guan Huaiyu Jian Richard Schoen
+ PDF Chat	Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space	2006	Bo Guan Huaiyu Jian Richard Schoen
+	Minimal submanifolds in higher codimension	2006	Richard Schoen
+	The mathematics of general relativity: problems and progress	2006	Richard Schoen
+ PDF Chat	KIDs are Non-Generic	2005	Robert Beig Piotr T. Chruściel Richard Schoen
+	On the Asymptotics for the Vacuum Einstein Constraint Equations	2003	Justin Corvino Richard Schoen
+ PDF Chat	Minimizing Area Among Lagrangian Surfaces: The Mapping Problem	2001	Richard Schoen Jon Wolfson
+	Minimizing area among Lagrangian surfaces: the mapping problem	2000	Richard Schoen Jon Wolfson
+ PDF Chat	Refined asymptotics for constant scalar curvature metrics with isolated singularities	1999	Nick Korevaar Rafe Mazzeo Frank Pacard Richard Schoen
+ PDF Chat	Recent Proofs of the Riemannian Penrose Conjecture	1999	Hubert L. Bray Richard Schoen
+	Theorems of Barth-Lefschetz type and Morse theory on the space of paths	1998	Richard Schoen Jon Wolfson
+	Minimizing volume among Lagrangian submanifolds	1998	Richard Schoen Jon Wolfson
+	Lectures on Harmonic Maps	1997	Richard Schoen Shing Tung Yau
+ PDF Chat	Global existence theorems for harmonic maps to non-locally compact spaces	1997	Nicholas J. Korevaari Richard Schoen
+	Symmetry Considerations, Topological Constraints, and Interactions with Physics	1996	Seiki Nishikawa Richard Schoen
+	Prescribed scalar curvature on then-sphere	1996	Richard Schoen Dong Zhang
+	Prescribed scalar curvature on the $n$ -sphere	1996	Richard Schoen Dong Zhang
+	On the conformal and CR automorphism groups	1995	Richard Schoen
+	On the Conformal and CR Automorphism Groups	1995	Richard Schoen
+	Lectures on Differential Geometry	1994	Richard Schoen Shing Tung Yau
+ PDF Chat	Sobolev spaces and harmonic maps for metric space targets	1993	Nicholas J. Korevaar Richard Schoen
+	Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one	1992	M. Gromov Richard Schoen
+	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	Hanspeter Kraft Gerald W. Schwarz Yves Benoist François Labourie G. Lusztig M. Gromov Richard Schoen
+	The theory and applications of harmonic mappings between riemannian manifolds	1992	Richard Schoen
+ PDF Chat	A report on some recent progress on non-linear problems in geometry	1990	Richard Schoen
+ PDF Chat	Variational theory for the total scalar curvature functional for riemannian metrics and related topics	1989	Richard Schoen
+	The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation	1988	Richard Schoen
+	Conformally flat manifolds, Kleinian groups and scalar curvature	1988	Richard Schoen Shing‐Tung Yau
+	The Structure of Manifolds with Positive Scalar Curvature	1987	Richard Schoen Shing‐Tung Yau
+	Conformal metrics with prescribed scalar curvature	1986	José F. Escobar Richard Schoen
+	New developments in the theory of geometric partial differential equations	1986	Richard Schoen Shiing-Shen Chern
+	The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature	1985	Hyeong In Choi Richard Schoen
+	Positive Harmonic Functions on Complete Manifolds of Negative Curvature	1985	Michael T. Anderson Richard Schoen
+	REGULARITY OF SIMPLY CONNECTED SURFACES WITH QUASICONFORMAL GAUSS MAP	1984	Richard Schoen L. Simon
+	Regularity of minimizing harmonic maps into the sphere	1984	Richard Schoen Karen Uhlenbeck
+	Analytic Aspects of the Harmonic Map Problem	1984	Richard Schoen
+ PDF Chat	Lp and mean value properties of subharmonic functions on Riemannian manifolds	1984	Peter Li Richard Schoen
+ PDF Chat	Conformal deformation of a Riemannian metric to constant scalar curvature	1984	Richard Schoen
+	On the isoperimetric inequality for minimal surfaces	1984	Peter Li Richard Schoen Shing‐Tung Yau
+ PDF Chat	Boundary regularity and the Dirichlet problem for harmonic maps	1983	Richard Schoen Karen Uhlenbeck
+ PDF Chat	Correction to: ``A regularity theory for harmonic maps''	1983	Richard Schoen Karen Uhlenbeck
+ PDF Chat	Uniqueness, symmetry, and embeddedness of minimal surfaces	1983	Richard Schoen
+	COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE	1982	Richard Schoen Shing‐Tung Yau
+	On the Gauss map of complete surfaces of constant mean curvature in R3 and R4	1982	David Hoffman Robert Osserman Richard Schoen
+	A remark on minimal hypercones	1982	Richard Schoen
+	On the existence of harmonic diffeomorphisms between surfaces	1982	Jürgen Jost Richard Schoen
+ PDF Chat	A regularity theory for harmonic maps	1982	Richard Schoen Karen Uhlenbeck
+ PDF Chat	A lower bound for the first eigenvalue of a negatively curved manifold	1982	Richard Schoen
+	Corrections to “compact group actions and the topology of manifolds with non-positive curvature”	1982	Richard Schoen Shing Tung Yau
+	Regularity of stable minimal hypersurfaces	1981	Richard Schoen Leon Simon
+	The structure of complete stable minimal surfaces in 3‐manifolds of non‐negative scalar curvature	1980	D. Fischer-Colbrie Richard Schoen
+	Geometric bounds on the low eigenvalues of a compact surface	1980	Richard Schoen Scott A. Wolpert S. T. Yau
+	Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature	1979	Richard Schoen Shing‐Tung Yau
+	Complete manifolds with nonnegative scalar curvature and the positive action conjecture in general relativity	1979	Richard Schoen Shing‐Tung Yau
+ PDF Chat	On the proof of the positive mass conjecture in general relativity	1979	Richard Schoen Shing-Tung Yau
+	On the structure of manifolds with positive scalar curvature	1979	Richard Schoen S.-T. Yau
+	Compact group actions and the topology of manifolds with non-positive curvature	1979	Richard Schoen Shing Tung Yau
+	On univalent harmonic maps between surfaces	1978	Richard Schoen Shing‐Tung Yau
+ PDF Chat	Incompressible minimal surfaces, three-dimensional manifolds with nonnegative scalar curvature, and the positive mass conjecture in general relativity	1978	Richard Schoen Shing‐Tung Yau
+	DETERMINING INSTALLED COSTS OF THE SAGE SYSTEM	1978	Richard Schoen Dale Furman
+ PDF Chat	Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals	1977	Richard Schoen L. Simon F. J. Almgren
+ PDF Chat	Curvature estimates for minimal hypersurfaces	1975	Richard Schoen L. Simon S.-T. Yau

Common Coauthors

Coauthor	Papers Together
Ailana Fraser	17
Shing‐Tung Yau	10
Simon Brendle	9
Shing Tung Yau	8
Huai-Dong Cao	5
Jon Wolfson	4
Karen Uhlenbeck	4
Jun Li	4
Lan-Hsuan Huang	4
Michael Eichmair	3
Yng-Ing Lee	3
L. Simon	3
Dominic Joyce	3
Alessandro Carlotto	3
Dan A. Lee	3
Robert Beig	3
Justin Corvino	2
Bo Guan	2
Peter Li	2
Hung Tran	2
Christos Mantoulidis	2
Huaiyu Jian	2
M. Gromov	2
S.-T. Yau	2
Mu‐Tao Wang	1
Jürgen Jost	1
S. T. Yau	1
Nicholas J. Korevaari	1
Robert Osserman	1
Camillo De Lellis	1
Rafe Mazzeo	1
Luciano de Simon	1
Dale Furman	1
Dong Zhang	1
Dong Zhang	1
Hung Tran	1
Hyeong In Choi	1
Shing-Tung Yau	1
Shiing-Shen Chern	1
Frank Pacard	1
F. J. Almgren	1
Suyu Cheng	1
José F. Escobar	1
Marcus Khuri	1
Leon Simon	1
Nick Korevaar	1
David Hoffman	1
D. Fischer-Colbrie	1
Seiki Nishikawa	1
Xin Zhou	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Multiple Integrals in the Calculus of Variations	1966	Charles B. Morrey	16
+ PDF Chat	On the proof of the positive mass conjecture in general relativity	1979	Richard Schoen Shing-Tung Yau	13
+	Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature	1979	Richard Schoen Shing‐Tung Yau	12
+	Geometric Measure Theory	1988	Herbert Fédérer	11
+	The Existence of Minimal Immersions of 2-Spheres	1981	J. Sacks Karen Uhlenbeck	10
+	The first Steklov eigenvalue, conformal geometry, and minimal surfaces	2010	Ailana Fraser Richard Schoen	9
+ PDF Chat	Inequalities for a Classical Eigenvalue Problem	1954	Robert Weinstock	9
+ PDF Chat	Four-manifolds with positive curvature operator	1986	Richard S. Hamilton	8
+	Minimal Two-Spheres and the Topology of Manifolds with Positive Curvature on Totally Isotropic Two-Planes	1988	Mario Micallef John Douglas Moore	8
+ PDF Chat	Four-manifolds with positive isotropic curvature	1997	Richard S. Hamilton	8
+ PDF Chat	Elliptic Partial Differential Equations of Second Order	2001	David Gilbarg Neil S. Trudinger	8
+ PDF Chat	Fundamental groups of manifolds with positive isotropic curvature	2003	Ailana Fraser	8
+ PDF Chat	Sharp eigenvalue bounds and minimal surfaces in the ball	2015	Ailana Fraser Richard Schoen	7
+ PDF Chat	Ricci deformation of the metric on a Riemannian manifold	1985	Gerhard Huisken	7
+ PDF Chat	Three-manifolds with positive Ricci curvature	1982	Richard S. Hamilton	7
+	The entropy formula for the Ricci flow and its geometric applications	2002	Grisha Perelman	7
+ PDF Chat	Group actions and curvature	1974	Karsten Grove Hermann Karcher Ernst A. Ruh	7
+	An equivariant pinching theorem	1975	Hans-Christoph Im Hof Ernst A. Ruh	7
+	A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces	1982	Peter Li Shing‐Tung Yau	7
+	Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung	1961	Wilhelm Klingenberg	7
+	Metrics with nonnegative isotropic curvature	1993	Mario Micallef McKenzie Y. Wang	7
+	Manifolds with 1/4-pinched curvature are space forms	2008	Simon Brendle Richard Schoen	7
+	Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations	2000	Justin Corvino	7
+ PDF Chat	Variational theory for the total scalar curvature functional for riemannian metrics and related topics	1989	Richard Schoen	7
+ PDF Chat	Riemannian manifolds with bounded curvature ratios	1982	Ernst A. Ruh	7
+ PDF Chat	Harmonic Maps of Manifolds with Boundary	1975	Richard S. Hamilton	7
+	The structure of complete stable minimal surfaces in 3‐manifolds of non‐negative scalar curvature	1980	D. Fischer-Colbrie Richard Schoen	7
+ PDF Chat	The splitting theorem for manifolds of nonnegative Ricci curvature	1971	Jeff Cheeger Detlef Gromoll	6
+	Harmonic Mappings of Riemannian Manifolds	1964	James Eells J. H. Sampson	6
+	Immersions minimales, première valeur propre du laplacien et volume conforme	1986	Ahmad El Soufi Saïd Ilias	6
+ PDF Chat	Conformal deformation of a Riemannian metric to constant scalar curvature	1984	Richard Schoen	6
+	Minimal Varieties in Riemannian Manifolds	1968	James Simons	6
+ PDF Chat	Linearization stability of the Einstein equations	1973	Arthur E. Fischer Jerrold E. Marsden	6
+	Geometric Measure Theory	1996	Herbert Fédérer	6
+ PDF Chat	Elliptic Partial Differential Equations of Second Order	1977	David Gilbarg Neil S. Trudinger	6
+ PDF Chat	On the Asymptotics for the Vacuum Einstein Constraint Equations	2006	Justin Corvino Richard Schoen	6
+ PDF Chat	An existence theorem for harmonic mappings of Riemannian manifolds	1977	Stefan Hildebrandt Helmut Kaul Kjell‐Ove Widman	6
+ PDF Chat	The mass of an asymptotically flat manifold	1986	Robert Bartnik	6
+ PDF Chat	Deforming metrics in the direction of their Ricci tensors	1983	Dennis DeTurck	5
+ PDF Chat	Einstein manifolds with nonnegative isotropic curvature are locally symmetric	2009	Simon Brendle	5
+	Remarks concerning the conformal deformation of riemannian structures on compact manifolds	1968	Neil S. Trudinger	5
+	Les variétés riemanniennes (1/4)-pincées	1960	Thomas Berger	5
+ PDF Chat	A short proof of Berger’s curvature tensor estimates	1970	Hermann Karcher	5
+	Analytic Aspects of the Harmonic Map Problem	1984	Richard Schoen	5
+ PDF Chat	On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications	2003	Piotr T. Chruściel Erwann Delay	5
+ PDF Chat	A regularity theory for harmonic maps	1982	Richard Schoen Karen Uhlenbeck	5
+	A Generalized Sphere Theorem	1977	Karsten Grove Katsuhiro Shiohama	5
+	The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation	1988	Richard Schoen	5
+	Deformations of the scalar curvature	1975	Arthur E. Fischer Jerrold E. Marsden	5
+ PDF Chat	A conformally invariant sphere theorem in four dimensions	2003	Sun‐Yung A. Chang Matthew J. Gursky Paul Yang	5