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Mathematics

D-Index
60
Citations
24713
World Ranking
537
National Ranking
276

Research.com Recognitions

  • 2017 - Rolf Schock Prize for Mathematics
  • 2017 - Wolf Prize in Mathematics for his contributions to geometric analysis and the understanding of the interconnectedness of partial differential equations and differential geometry.
  • 2013 - Fellow of the American Mathematical Society
  • 1996 - Fellow of John Simon Guggenheim Memorial Foundation
  • 1994 - Fellow of the American Association for the Advancement of Science (AAAS)
  • 1991 - Member of the National Academy of Sciences
  • 1988 - Fellow of the American Academy of Arts and Sciences
  • 1979 - Fellow of Alfred P. Sloan Foundation

Overview

Richard Schoen is affiliated with the University of California, Irvine, United States. Their research primarily falls within the field of Mathematics, with a focus on subfields such as Applied Mathematics, Geometry and Topology, Computational Theory and Mathematics, and Mathematical Physics.

The main topics they have worked on include:

  • Geometric Analysis and Curvature Flows
  • Geometry and complex manifolds
  • Nonlinear Partial Differential Equations
  • Advanced Mathematical Modeling in Engineering
  • Geometric and Algebraic Topology
  • Homotopy and Cohomology in Algebraic Topology

Recent publications highlight collaboration and a focus on partial differential equations and geometric analysis. Some notable papers are:

  • "Partial Differential Equations," 2020, Oberwolfach Reports
  • "Some results on higher eigenvalue optimization," 2020, Calculus of Variations and Partial Differential Equations
  • "Partial Differential Equations," 2022, Oberwolfach Reports
  • "Preface to Peter Li Volume," 2022, Journal of Geometric Analysis
  • "Stability and largeness properties of minimal surfaces in higher codimension," 2023, arXiv (Cornell University)

Frequent co-authors working with Schoen include:

  • Ailana Fraser
  • Guido De Philippis
  • Peter M. Topping
  • Felix Schulze
  • Jaigyoung Choe

Publishing venues where Schoen's work often appears are:

  • arXiv (Cornell University)
  • Oberwolfach Reports
  • Calculus of Variations and Partial Differential Equations
  • Journal of Geometric Analysis
  • Journal of the European Mathematical Society

Throughout their career, Schoen has received several awards and honors, including:

  • Rolf Schock Prize for Mathematics (2017)
  • Wolf Prize in Mathematics (2017) for contributions to geometric analysis and the understanding of interconnected partial differential equations and differential geometry
  • Fellow of the American Mathematical Society (2013)
  • Fellow of John Simon Guggenheim Memorial Foundation (1996)
  • Fellow of the American Association for the Advancement of Science (AAAS) (1994)
  • Member of the National Academy of Sciences (1991)
  • Fellow of the American Academy of Arts and Sciences (1988)
  • Fellow of Alfred P. Sloan Foundation (1979)

Best Publications

  • Conformal deformation of a Riemannian metric to constant scalar curvature

    Richard Schoen

  • On the proof of the positive mass conjecture in general relativity

    Richard Schoen;Shing Tung Yau

  • Lectures on Differential Geometry

    Richard M. Schoen;Shing Tung Yau

  • The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature

    Doris Fischer-Colbrie;Richard Schoen

  • A regularity theory for harmonic maps

    Richard Schoen;Karen Uhlenbeck

  • Proof of the positive mass theorem. II

    Richard Schoen;Shing Tung Yau

  • Variational theory for the total scalar curvature functional for riemannian metrics and related topics

    Richard M. Schoen

  • On the structure of manifolds with positive scalar curvature

    Richard Schoen;Shing-Tung Yau

  • Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature

    R. Schoen;Shing-Tung Yau

  • Sobolev spaces and harmonic maps for metric space targets

    Nicholas J. Korevaar;Richard M. Schoen

  • Harmonic maps into singular spaces and $p$ -adic superrigidity for lattices in groups of rank one

    Mikhail Gromov;Richard Schoen

  • Boundary regularity and the Dirichlet problem for harmonic maps

    Richard Schoen;Karen Uhlenbeck

  • Conformally flat manifolds, Kleinian groups and scalar curvature

    R. Schoen;S. T. Yau

  • Uniqueness, symmetry, and embeddedness of minimal surfaces

    Richard M. Schoen

  • Curvature estimates for minimal hypersurfaces

    R. Schoen;L. Simon;S. T. Yau

  • Manifolds with 1/4-pinched curvature are space forms

    Simon Brendle;Richard M. Schoen

  • Regularity of stable minimal hypersurfaces

    Richard Schoen;Leon Simon

  • A Generalization of Hawking's Black Hole Topology Theorem to Higher Dimensions

    Gregory J. Galloway;Richard Schoen

  • Lectures on Harmonic Maps

    Richard M. Schoen;Shing Tung Yau

  • Analytic Aspects of the Harmonic Map Problem

    Richard M. Schoen

Frequent Co-Authors

Shing-Tung Yau
Shing-Tung Yau Tsinghua University
Simon Brendle
Simon Brendle Columbia University
Leon Simon
Leon Simon Stanford University
Karen Uhlenbeck
Karen Uhlenbeck The University of Texas at Austin
Dominic Joyce
Dominic Joyce University of Oxford
Mikhael Gromov
Mikhael Gromov Institut des Hautes Études Scientifiques
Jürgen Jost
Jürgen Jost Max Planck Institute for Mathematics in the Sciences
Rafe Mazzeo
Rafe Mazzeo Stanford University
Piotr T. Chruściel
Piotr T. Chruściel University of Vienna
Gary W. Gibbons
Gary W. Gibbons University of Cambridge

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