##### Department of Mathematics,

University of California San Diego

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### Joint UCI-UCSD Geometry Seminar

## Jacob Bernstein

#### Massachusetts Institute of Technology

## Helicoid-Like Minimal Disks

##### Abstract:

Colding and Minicozzi have shown that if an embedded minimal disk in $B_R\subset\mathbb{R}^3$ has large curvature then in a smaller ball, on a scale still proportional to $R$, the disk looks roughly like a piece of a helicoid. In this talk, we will see that near points whose curvature is relatively large the description can be made more precise. That is, in a neighborhood of such a point (on a scale $s$ proportional to the inverse of the curvature of the point) the surface is bi-Lipschitz to a piece of a helicoid. Moreover, the Lipschitz constant goes to 1 as $Rs$ goes to $\infty$ . This follows from Meeks and Rosenberg's result on the uniqueness of the helicoid of which, time permitting, we will discuss a new proof. Joint work with C. Breiner.

Hosts: Ben Weinkove and Lei Ni

### December 3, 2008

### 4:00 PM

### AP&M 6402

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