• Publications
  • Influence
Generic mean curvature flow I; generic singularities
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 theExpand
  • 386
  • 62
  • PDF
The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected
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 ofExpand
  • 131
  • 25
  • PDF
A Course in Minimal Surfaces
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 differentialExpand
  • 201
  • 24
The Calabi-Yau conjectures for embedded surfaces
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 theExpand
  • 141
  • 22
  • PDF
HARMONIC FUNCTIONS ON MANIFOLDS
  • 130
  • 20
  • PDF
The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus
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 embeddedExpand
  • 82
  • 15
  • PDF
Uniqueness of blowups and Łojasiewicz inequalities
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 weaklyExpand
  • 79
  • 15
  • PDF
The space of embedded minimal surfaces of fixed genus in a 3-manifold I; Estimates off the axis for disks
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 suchExpand
  • 99
  • 14
  • PDF
The space of embedded minimal surfaces of fixed genus in a 3-manifold II; Multi-valued graphs in disks
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 understandingExpand
  • 103
  • 13
  • PDF
Smooth compactness of self-shrinkers
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 aExpand
  • 87
  • 12
  • PDF