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Publications Influence

Generic mean curvature flow I; generic singularities

- T. Colding, W. Minicozzi
- Mathematics
- 26 August 2009

It has long been conjectured that starting at a generic smooth closed embedded surface in R^3, the mean curvature flow remains smooth until it arrives at a singularity in a neighborhood of which the… Expand

384 60- PDF

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

- J. Cheeger, T. Colding
- Mathematics
- 2000

In this paper and in we study the structure of spaces Y which are pointed Gromov Hausdor limits of sequences f M i pi g of complete connected Riemannian manifolds whose Ricci curvatures have a de… Expand

627 59

Ricci curvature and volume convergence

- T. Colding
- Mathematics
- 1 May 1997

The purpose of this paper is to give a new (integral) estimate of distances and angles on manifolds with a given lower Ricci curvature bound. This will provide us with an integral version of the… Expand

200 26

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

- T. Colding, W. Minicozzi
- Mathematics
- 8 October 2002

This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3manifold. The key is to understand the structure of… Expand

131 25- PDF

A Course in Minimal Surfaces

- T. Colding, W. Minicozzi
- Mathematics
- 1 April 2011

Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential… Expand

201 24

The Calabi-Yau conjectures for embedded surfaces

- T. Colding, W. Minicozzi
- Mathematics
- 9 April 2004

In this talk I will discuss the proof of the Calabi-Yau conjectures for embedded surfaces. This is joint work with Bill Minicozzi, [CM9]. The Calabi-Yau conjectures about surfaces date back to the… Expand

141 22- PDF

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

- T. Colding, A. Naber
- Mathematics
- 24 February 2011

We prove a new estimate on manifolds with a lower Ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a Holder continuous way along the… Expand

131 17- PDF

The min--max construction of minimal surfaces

- T. Colding, C. D. Lellis
- Mathematics
- 25 March 2003

In this paper we survey with complete proofs some well-known, but hard to find, results about constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min-max arguments.… Expand

108 17- PDF

The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus

- T. Colding, W. Minicozzi
- Mathematics
- 27 September 2005

This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for \itnonsimply connected embedded… Expand

83 15- PDF