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

2012/06/29 by Simon Raulot, Raulot, Simon, Alessandro Savo +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.1206.7102

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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• Scaling inequalities for Steklov eigenvalues in space forms and sharp eigenvalue estimates on warped product manifolds

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