Sharp bounds for the first eigenvalue of a fourth order Steklov problem

Simon Raulot; Alessandro Savo

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arXiv · 1206.7102

Sharp bounds for the first eigenvalue of a fourth order Steklov problem

Simon Raulot·Alessandro Savo

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Abstract

We study the biharmonic Steklov eigenvalue problem on a compact Riemannian manifold $Ω$ with smooth boundary. We give a computable, sharp lower bound of the first eigenvalue of this problem, which depends only on the dimension, a lower bound of the Ricci curvature of the domain, a lower bound of the mean curvature of its boundary and the inner radius. The proof is obtained by estimating the isoperimetric ratio of non-negative subharmonic functions on $Ω$, which is of independent interest. We also give a comparison theorem for geodesic balls.

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Simon Raulot, Alessandro Savo. 2012-06-29. Sharp bounds for the first eigenvalue of a fourth order Steklov problem. https://arxiv.org/abs/1206.7102

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