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The Steklov spectrum of surfaces: asymptotics and invariants

Published online by Cambridge University Press:  19 August 2014

ALEXANDRE GIROUARD ,
LEONID PARNOVSKI ,
IOSIF POLTEROVICH  and
DAVID A. SHER
ALEXANDRE GIROUARD
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, 1045, av. de la Médecine, Québec Qc G1V 0A6, Canada. e-mail: [email protected]
LEONID PARNOVSKI
Affiliation:
Department of Mathematics, University College London, Gower Street, LondonWC1E 6BT. e-mail: [email protected]
IOSIF POLTEROVICH
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, CP 6128 succ Centre-Ville, Montréal QC H3C 3J7, Canada. e-mail: [email protected]
DAVID A. SHER
Affiliation:
Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043, U.S.A. e-mail: [email protected]
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Abstract

We obtain precise asymptotics for the Steklov eigenvalues on a compact Riemannian surface with boundary. It is shown that the number of connected components of the boundary, as well as their lengths, are invariants of the Steklov spectrum. The proofs are based on pseudodifferential techniques for the Dirichlet-to-Neumann operator and on a number–theoretic argument.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 3 , November 2014 , pp. 379 - 389
Copyright
Copyright © Cambridge Philosophical Society 2014 

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