##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Elia Brue

## Boundary regularity and stability for spaces with Ricci curvature bounded below

##### Abstract:

The theory of RCD spaces has seen a huge development in the last teen years. They are metric measure structures satisfying a synthetic notion of Ricci bounded below. This class includes several spaces with boundary, such as Gromov-Hausdorff limits of manifolds with convex boundary and Ricci bounded below in the interior. In this talk we will present new stability and regularity results for boundaries of RCD spaces. We will focus mostly on a new epsilon-regularity theorem which is new even in the setting of smooth Riemannian manifolds. It is based on a work in progress joint with Aaron Naber and Daniele Semola.

Host: Lei Ni and Luca Spolaor

### October 14, 2020

### 11:00 AM

### Zoom ID: 960 7952 5041

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