SMS scnews item created by Daniel Daners at Thu 22 Aug 2019 1424
Type: Seminar
Distribution: World
Expiry: 26 Aug 2019
Calendar1: 26 Aug 2019 1200-1300
CalLoc1: AGR Carslaw 829
CalTitle1: PDE Seminar: The Brunn-Minkowski inequality for the Monge-Ampere eigenvalue and smoothness of the eigenfunctions (Le)
Auth: daners@dora.maths.usyd.edu.au

# The Brunn-Minkowski inequality for the Monge-Ampere eigenvalue and smoothness of the eigenfunctions

### Le

Nam Quang Le
Indiana University, USA
Mon 26th Aug 2019, 12-1pm, Carslaw Room 829 (AGR)

## Abstract

The original form of the Brunn-Minkowski inequality involves volumes of convex bodies in ${ℝ}^{n}$ and states that the $n$-th root of the volume is a concave function with respect to the Minkowski addition of convex bodies.

In 1976, Brascamp and Lieb proved a Brunn-Minkowski inequality for the first eigenvalue of the Laplacian. In this talk, I will discuss a nonlinear analogue of the above result, that is, the Brunn-Minkowski inequality for the eigenvalue of the Monge-Ampère operator. For this purpose, I will first introduce the Monge-Ampère eigenvalue problem on general bounded convex domains. Then, I will present several properties of the eigenvalues and related analysis concerning smoothness of the eigenfunctions.

For Seminar announcements you can now subscribe to the Seminar RSS feed. Check also the PDE Seminar page.

Enquiries to Daniel Hauer or Daniel Daners.

If you are registered you may mark the scnews item as read.
School members may try to .