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Lower bounds on Ricci curvature and the almost rigidity of warped products
- J. Cheeger, T. Colding
- Mathematics
- 1 July 1996
The basic rigidity theorems for manifolds of nonnegative or positive Ricci curvature are the "volume cone implies metric cone" theorem, the maximal diameter theorem, [Cg], and the splitting theorem,…
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…
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…
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…
HARMONIC FUNCTIONS ON MANIFOLDS
- T. Colding, W. Minicozzi
- Mathematics
- 1 November 1997
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…
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…
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…
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…
The min--max construction of minimal surfaces
- T. Colding, C. 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.…
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