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Spectral rigidity and invariant distributions on Anosov surfaces

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Paternain, G. P., Salo, M., & Uhlmann, G. (2014). Spectral rigidity and invariant distributions on Anosov surfaces. Journal of differential geometry, 98(1), 147-181. https://doi.org/10.4310/jdg/1406137697
Published in
Journal of differential geometry
Authors
Paternain, Gabriel P. |
Salo, Mikko |
Uhlmann, Gunther
Date
2014
Discipline
MatematiikkaMathematics
Copyright
© The Authors. © Lehigh University, 2014. This is an authors' final draft version of an article whose final and definitive form has been published by Lehigh University. Published in this repository with the kind permission of the publisher.

 
This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface (M,g), given a smooth function f on M there is a distribution in the Sobolev space H-1(SM) that is invariant under the geodesic flow and whose projection to M is the given function f.
Publisher
Lehigh University
ISSN Search the Publication Forum
0022-040X
Keywords
conjugate-points isospectral manifolds

Original source
http://projecteuclid.org/euclid.jdg/1406137697

DOI
https://doi.org/10.4310/jdg/1406137697
URI

http://urn.fi/URN:NBN:fi:jyu-201501091064

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/23817354

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