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Tobias H. Colding

Tobias H. Colding

D-Index & Metrics

Mathematics

D-Index
41
Citations
9519
World Ranking
1873
National Ranking
799

Research.com Recognitions

  • 2008 - Fellow of the American Academy of Arts and Sciences
  • 1996 - Fellow of Alfred P. Sloan Foundation

Overview

Tobias H. Colding is affiliated with MIT in the United States and contributes extensively to the field of mathematics. Their research focuses predominantly on applied mathematics, geometry and topology, and mathematical physics, alongside subfields such as astronomy, astrophysics, and computational theory related to mathematics.

The scholar's work is categorized under several main topics, including:

  • Geometric Analysis and Curvature Flows
  • Geometry and complex manifolds
  • Nonlinear Partial Differential Equations
  • Mathematical Dynamics and Fractals
  • Advanced Differential Geometry Research
  • Advanced Operator Algebra Research
  • Geometric and Algebraic Topology

They frequently publish in notable venues such as:

  • Journal für die reine und angewandte Mathematik (Crelles Journal)
  • arXiv (Cornell University)
  • Publications mathématiques de l IHÉS
  • Advanced Nonlinear Studies
  • Duke Mathematical Journal

Recent papers authored by Tobias H. Colding include:

  • Optimal bounds for ancient caloric functions, 2021, Duke Mathematical Journal
  • Complexity of parabolic systems, 2020, Publications mathématiques de l IHÉS
  • Regularity of elliptic and parabolic systems, 2024, Annales Scientifiques de l'École Normale Supérieure
  • Wandering singularities, 2021, Journal of Differential Geometry
  • Singularities and diffeomorphisms, 2022, Notices of the International Consortium of Chinese Mathematicians

The list of frequent co-authors includes:

  • Daniel Huybrechts
  • Jun-Muk Hwang
  • Joachim Cuntz
  • David Masser
  • Franz Stückle

Their publication record encompasses 54 papers primarily in mathematics, with 27 focused on applied mathematics, 15 on geometry and topology, and 12 on mathematical physics.

Awards received by Tobias H. Colding include:

  • Fellow of the American Academy of Arts and Sciences, 2008
  • Fellow of Alfred P. Sloan Foundation, 1996

Best Publications

  • On the structure of spaces with Ricci curvature bounded below. I

    Jeff Cheeger;Tobias H. Colding

  • Lower bounds on Ricci curvature and the almost rigidity of warped products

    Jeff Cheeger;Tobias H. Colding

  • Generic mean curvature flow I; generic singularities

    Tobias H. Colding;William P. Minicozzi

  • Ricci curvature and volume convergence

    Tobias H. Colding

  • A Course in Minimal Surfaces

    Tobias H. Colding;William P. Minicozzi

  • Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

    Tobias Colding;Aaron Charles Naber

  • On the singularities of spaces with bounded Ricci curvature

    J. Cheeger;T.H. Colding;G. Tian

  • HARMONIC FUNCTIONS ON MANIFOLDS

    Tobias H. Colding;William P. Minicozzi

  • The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected

    Tobias H. Colding;William P. Minicozzi

  • The Calabi-Yau conjectures for embedded surfaces

    Tobias H. Colding;William P. Minicozzi

  • The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks

    Tobias H. Colding;William P. Minicozzi

  • The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks

    Tobias H. Colding;William P. Minicozzi

  • Uniqueness of blowups and Łojasiewicz inequalities

    Tobias Holck Colding;William P. Minicozzi

  • Shape of manifolds with positive Ricci curvature

    Tobias H. Colding

  • Harmonic functions with polynomial growth

    Tobias H. Colding;William P. Minicozzi

  • The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains

    Tobias H. Colding;William P. Minicozzi

  • Large manifolds with positive Ricci curvature

    Tobias H. Colding

  • LIOUVILLE THEOREMS FOR HARMONIC SECTIONS AND APPLICATIONS

    Tobias H. Colding;William P. Minicozzi

  • Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman

    Tobias H. Colding;William P. Minicozzi

  • Smooth compactness of self-shrinkers

    Tobias H. Colding;William P. Minicozzi Ii

  • The min--max construction of minimal surfaces

    Tobias H. Colding;Camillo De Lellis

Frequent Co-Authors

Jeff Cheeger
Jeff Cheeger Courant Institute of Mathematical Sciences
Camillo De Lellis
Camillo De Lellis Institute for Advanced Study
Bruce Kleiner
Bruce Kleiner Courant Institute of Mathematical Sciences
Gang Tian
Gang Tian Peking University
Brian White
Brian White Stanford University
Stevo Todorcevic
Stevo Todorcevic University of Toronto

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