- Home
- Best Scientists - Mathematics
- Tobias H. Colding

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
38
Citations
8,362
111
World Ranking
1537
National Ranking
683

2008 - Fellow of the American Academy of Arts and Sciences

1996 - Fellow of Alfred P. Sloan Foundation

- Mathematical analysis
- Geometry
- Pure mathematics

Tobias H. Colding mainly focuses on Mathematical analysis, Ricci curvature, Curvature, Scalar curvature and Minimal surface. His work on Harmonic function, Subharmonic function and Geodesic as part of general Mathematical analysis research is frequently linked to Anharmonicity, thereby connecting diverse disciplines of science. His specific area of interest is Scalar curvature, where Tobias H. Colding studies Curvature of Riemannian manifolds.

In his research on the topic of Curvature of Riemannian manifolds, Mathematical physics, Sectional curvature and Ricci flow is strongly related with Riemann curvature tensor. His work deals with themes such as Algebra, 3-manifold, Simply connected space, Injective function and Differential geometry, which intersect with Minimal surface. His Ricci decomposition study integrates concerns from other disciplines, such as Mean curvature and Mean curvature flow.

- On the structure of spaces with Ricci curvature bounded below. I (789 citations)
- Lower bounds on Ricci curvature and the almost rigidity of warped products (447 citations)
- Generic mean curvature flow I; generic singularities (327 citations)

Tobias H. Colding mostly deals with Mathematical analysis, Pure mathematics, Minimal surface, Ricci curvature and Mean curvature flow. His Mathematical analysis research incorporates elements of Flow and Mean curvature, Curvature. Tobias H. Colding focuses mostly in the field of Pure mathematics, narrowing it down to topics relating to Uniqueness and, in certain cases, Monotone polygon.

His Ricci curvature research is multidisciplinary, incorporating perspectives in Curvature of Riemannian manifolds, Scalar curvature, Combinatorics and Manifold. His study in Curvature of Riemannian manifolds is interdisciplinary in nature, drawing from both Riemann curvature tensor and Ricci-flat manifold. As a member of one scientific family, Tobias H. Colding mostly works in the field of Mean curvature flow, focusing on Gravitational singularity and, on occasion, Singularity, Lipschitz continuity and Conjecture.

- Mathematical analysis (50.98%)
- Pure mathematics (37.91%)
- Minimal surface (26.14%)

- Pure mathematics (37.91%)
- Gravitational singularity (21.57%)
- Mathematical analysis (50.98%)

The scientist’s investigation covers issues in Pure mathematics, Gravitational singularity, Mathematical analysis, Flow and Mean curvature flow. His work in the fields of Minimal surface overlaps with other areas such as Ornstein–Uhlenbeck operator. His work in Gravitational singularity addresses issues such as Singularity, which are connected to fields such as Special case and Hypersurface.

His Second derivative and Differentiable function study in the realm of Mathematical analysis connects with subjects such as Nonlinear system and Set. Tobias H. Colding works mostly in the field of Mean curvature flow, limiting it down to concerns involving Codimension and, occasionally, Subspace topology and Euclidean geometry. His Bounded function research is multidisciplinary, relying on both Manifold, Harmonic function and Conjecture.

- The singular set of mean curvature flow with generic singularities (22 citations)
- Optimal bounds for ancient caloric functions (16 citations)
- Level Set Method For Motion by Mean Curvature (12 citations)

- Mathematical analysis
- Geometry
- Pure mathematics

Tobias H. Colding mainly investigates Pure mathematics, Gravitational singularity, Bounded function, Mean curvature flow and Singularity. Tobias H. Colding has researched Pure mathematics in several fields, including Lamination and Sectional curvature. His Bounded function study incorporates themes from Codimension, Harmonic function and Conjecture.

His biological study spans a wide range of topics, including Dimension, Degree, Constant, Polynomial and Ricci curvature. His Conjecture research includes elements of Space and Manifold. Tobias H. Colding interconnects Hypersurface and Lipschitz continuity in the investigation of issues within Mean curvature flow.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

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

Jeff Cheeger;Tobias H. Colding.

Journal of Differential Geometry **(2000)**

1363 Citations

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

Jeff Cheeger;Tobias H. Colding.

Annals of Mathematics **(1996)**

757 Citations

Generic mean curvature flow I; generic singularities

Tobias H. Colding;William P. Minicozzi.

Annals of Mathematics **(2012)**

562 Citations

Ricci curvature and volume convergence

Tobias H. Colding.

Annals of Mathematics **(1997)**

409 Citations

A Course in Minimal Surfaces

Tobias H. Colding;William P. Minicozzi.

**(2011)**

292 Citations

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

Tobias Colding;Aaron Charles Naber.

Annals of Mathematics **(2012)**

289 Citations

On the singularities of spaces with bounded Ricci curvature

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

Geometric and Functional Analysis **(2002)**

282 Citations

HARMONIC FUNCTIONS ON MANIFOLDS

Tobias H. Colding;William P. Minicozzi.

Annals of Mathematics **(1997)**

239 Citations

The Calabi-Yau conjectures for embedded surfaces

Tobias H. Colding;William P. Minicozzi.

Annals of Mathematics **(2008)**

223 Citations

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

Tobias H. Colding;William P. Minicozzi.

Annals of Mathematics **(2004)**

220 Citations

If you think any of the details on this page are incorrect, let us know.

Contact us

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Courant Institute of Mathematical Sciences

Institute for Advanced Study

Peking University

Courant Institute of Mathematical Sciences

Stanford University

ETH Zurich

New York University

Nokia (United States)

Technion – Israel Institute of Technology

University of Ulsan

University of Augsburg

National Marine Fisheries Service

Texas A&M University

Centers for Disease Control and Prevention

University of Hawaii at Manoa

Karlsruhe Institute of Technology

University of Oregon

Northeastern University

The University of Texas MD Anderson Cancer Center

University of Cincinnati

University of London

University of Denver

Something went wrong. Please try again later.