A disc maximizes Laplace eigenvalues among isoperimetric surfaces of revolution

2014/10/07 by Sinan Ariturk, Ariturk, Sinan
Mathematics · #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Point processes and geometric inequalities #math.AP #math.DG #msc:35P15

paper · pdf · doi:10.48550/arxiv.1410.1847

arxiv created 2014/10/07 · arxiv updated 2014/10/08

Abstract

The Dirichlet eigenvalues of the Laplace-Beltrami operator are larger on a flat disc than on any other surface of revoltuion immersed in Euclidean space with the same boundary.

Citations

• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

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