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Local audibility of a hyperbolic metric

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Abstract

A Riemannian metric g on a compact boundaryless manifold is said to be locally audible if the following statement is true for every metric g′ sufficiently close to g: if g and g′ are isospectral then they are isometric. The local audibility is proved of a metric of constant negative sectional curvature.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Vladimir A. Sharafutdinov

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  1. Vladimir A. Sharafutdinov
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Correspondence to Vladimir A. Sharafutdinov.

Additional information

To Yuriĭ Grigor’evich Reshetnyak on his 80th birthday.

Original Russian Text Copyright © 2009 Sharafutdinov V. A.

The author was supported by the Russian Foundation for Basic Research (Grant 08-01-92001-NNS) and the Integration Project of the Siberian Division of the Russian Academy of Sciences (Grant No. 94).

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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 5, pp. 1176–1194, September–October, 2009.

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Sharafutdinov, V.A. Local audibility of a hyperbolic metric. Sib Math J 50, 929–944 (2009). https://doi.org/10.1007/s11202-009-0103-7

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  • DOI: https://doi.org/10.1007/s11202-009-0103-7

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