The Size of Isospectral Families

  • Peter Buser
Part of the Modern Birkhäuser Classics book series (MBC)


McKean [1] 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.


Universal Covering Boundary Component Closed Geodesic Compact Riemann Surface Compact Riemannian Manifold 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Département de MathématiquesEcole Polytechnique Fédérale de LausanneLausanne-EcublensSwitzerland

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