26 citations · 99 across the 14 of their papers we have counts for
7 papers · 1 filter
Minimal submanifolds
Tobias H. Colding, William P. Minicozzi
In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.
The Calabi-Yau conjectures for embedded surfaces
Tobias H. Colding, William P. Minicozzi
In this paper we will prove the Calabi-Yau conjectures for embedded surfaces. In fact, we will prove considerably more. The Calabi-Yau conjectures about surfaces date back to the 1…
Singularity structure in mean curvature flow of mean convex sets
Tobias H. Colding, Bruce Kleiner
In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow wher…
Embedded minimal disks: Proper versus nonproper - global versus local
Tobias H. Colding, William P. Minicozzi
We construct a sequence of embedded minimal disks in a ball where the curvatures blow up only at the center. The sequence converges to a limit which is not smooth and not proper.
Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics
Tobias H. Colding, Nancy Hingston
We give in this paper bounds for the Morse indices of a large class of simple geodesics on a surface with a generic metric. To our knowledge these bounds are the first that use onl…
Singular limit laminations, Morse index, and positive scalar curvature
Tobias H. Colding, Camillo De Lellis
For any 3-manifold M and any nonnegative integer g, we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus g and without Morse ind…