26 citations · 97 across the 9 of their papers we have counts for
11 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…
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…
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.
The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains
Tobias H. Colding, William P. Minicozzi
This paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3-manifold. In [CM3]-[CM5] we desc…