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.
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