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Isaac Newton Institute for Mathematical Sciences

Symmetry tricks in spectral geometry

2nd August 2006

Author: Levitin, M (Heriot-Watt University)

Abstract

We show the use of symmetry tricks in solving two problems of spectral geometry. One is a partial case g=2 of the question ''How large can the first eigenvalue be on a surface of genus g?'' Another is a modification of the famous Mark Kac's question, ''Can one hear the shape of a drum?'' The questions (or, rather, our answers) are suprisingly related