26 citations · 99 across the 14 of their papers we have counts for
15 papers
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…
Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman
Tobias H. Colding, William P. Minicozzi
In this note we prove some bounds for the extinction time for the Ricci flow on certain 3-manifolds. Our interest in this comes from a question of Grisha Perelman asked to the firs…
Sharp estimates for mean curvature flow of graphs
Tobias H. Colding, W. P. Minicozzi
Sharp estimates for mean curvature flow of graphs are shown and examples are given to illustrate why these are sharp. The estimates improves earlier (non-sharp) estimates of Klaus…
The min--max construction of minimal surfaces
Tobias H. Colding, Camillo De Lellis
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…