##### Department of Mathematics,

University of California San Diego

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### Joint UCI-UCR-UCSD Southern California Differential Geometry Seminar

## Xin Zhou

#### UCSB

## Min-max minimal hypersurfaces with free boundary

##### Abstract:

I will present a joint work with Martin Li. Minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. In this talk, I will describe a general existence theory for minimal surfaces with free boundary. In particular, I will show the existence of a smooth embedded minimal hypersurface with free boundary in any compact smooth Euclidean domain. The minimal surfaces with free boundary were constructed using the min-max method. I will explain the basic ideas behind the min-max theory as well as our new contributions.

### November 3, 2016

### 3:00 PM

### UC Irvine, Rolland Hall, Room 306

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