##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Giuseppe Tinaglia

#### Stanford University

## Structure theorems for disks embedded in $R^3$

##### Abstract:

In this talk we will discuss the shape of embedded disks with bounded mean curvature. In particular, we will prove that an embedded disk with bounded mean curvature and Gaussian curvature large at a point contains a multi-valued graph around that point on the scale of the norm square of the II fundamental form. Roughly speaking, it looks like helicoids. This generalizes Colding and Minicozzi's result for minimal surfaces.

Host: Neshan Wickramasekera

### September 28, 2005

### 4:00 PM

### AP&M 5829

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