##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Max Engelstein

#### University of Minnesota

## The Riemannian Quantitative Isoperimetric Inequality

##### Abstract:

The (Euclidean) isoperimetric inequality says that any set has larger perimeter than a ball with the same area. The quantitative isoperimetric inequality says that the difference in perimeters is bounded from below by the square of the distance from our set E to the ``closest'' ball of the same area. In this talk, we will discuss an extension of this result to closed Riemannian manifolds with analytic metrics. In particular, we show that a similar inequality holds but with the distance raised to a power that depends on the geometry. We also have examples which show that a greater power than two is sometimes necessary and that the analyticity condition is necessary. This is joint work with O. Chodosh (Stanford) and L. Spolaor (UCSD).

Host: Lei Ni

### February 12, 2020

### 10:00 AM

### AP&M 6402

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