The Size of Isospectral Families
McKean  has shown that only finitely many compact Riemann surfaces have a given spectrum. In this chapter we give an explicit bound which depends only on the genus. The proof covers Sections 13.2 - 13.4. In the first section we state the result and give a proof of McKean’s theorem in order to outline the approach. In the first section we also review the necessary material from earlier chapters.
KeywordsUniversal Covering Boundary Component Closed Geodesic Compact Riemann Surface Compact Riemannian Manifold
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