### Geometric excess of the fundamental gap

Analysis and Geometry Seminar

26th March 2024, 3:00 pm – 4:00 pm

Fry Building, Room 2.04

On convex sets of $R^N$ the Payne-Weinberger and Andrews-Clutterbuck inequalities provide sharp lower bounds of the fundamental gap of the Laplace operator with Neumann and Dirichlet boundary conditions, respectively, in terms of the diameter. For $N \ge 2$ the bounds are not attained and are improved with a geometric term related to the flatness of the convex set. This is a joint work with V. Amato and I. Fragala.

## Comments are closed.