##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Gabor Szekelyhidi

#### Notre Dame

## Uniqueness of certain cylindrical tangent cones

##### Abstract:

Leon Simon showed that if an area minimizing hypersurface admits a cylindrical tangent cone of the form C x R, then this tangent cone is unique for a large class of minimal cones C. One of the hypotheses in this result is that C x R is integrable and this excludes the case when C is the Simons cone over $S^3 x S^3$. The main result in this talk is that the uniqueness of the tangent cone holds in this case too. The new difficulty in this non-integrable situation is to develop a version of the Lojasiewicz-Simon inequality that can be used in the setting of tangent cones with non-isolated singularities.

Host: Lei Ni

### December 2, 2020

### 10:00 AM

### Zoom ID: 960 7952 5041

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