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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

386 62- PDF

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

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

82 15- PDF

Uniqueness of blowups and Łojasiewicz inequalities

- T. Colding, W. Minicozzi
- Mathematics
- 14 December 2013

Once one knows that singularities occur, one naturally wonders what the singu- larities are like. For minimal varieties the first answer, already known to Federer-Fleming in 1959, is that they weakly… Expand

79 15- PDF

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

- T. Colding, W. Minicozzi
- Physics, Mathematics
- 7 October 2002

This paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such… Expand

99 14- PDF

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

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

This paper is the second in a series where we give a description of the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. The key for understanding… Expand

103 13- PDF

Smooth compactness of self-shrinkers

- T. Colding, W. Minicozzi
- Mathematics
- 15 July 2009

We prove a smooth compactness theorem for the space of embedded self-shrinkers in $\RR^3$. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a… Expand

87 12- PDF