### Bounds for Steklov eigenvalues of warped products

Analysis and Geometry Seminar

15th February 2024, 3:30 pm – 4:30 pm

Fry Building, Room 2.04

I will give sharp upper bounds for the Steklov eigenvalues of warped product between an interval [0, L] and a compact Riemannian manifold of dimension 2. I will also consider the case of revolution metrics on the ball of dimension n. In this situation, I will give sharp upper bound for the ratio of two consecutive eigenvalues, in the sense of a Payne-Polya-Weinberger inequality, and, in dimension 3, for the gap between two consecutive eigenvalues. These results are obtained in collaboration with Jade Brisson and Katie Gittins.

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