SPECTRAL RIGIDITY AND INVARIANT DISTRIBUTIONS ON ANOSOV SURFACES
Accepted version
Peer-reviewed
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Authors
Paternain, Gabriel P
Salo, Mikko
Uhlmann, Gunther
Abstract
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
Description
Keywords
math.DG, math.DG, math.AP, math.DS
Journal Title
JOURNAL OF DIFFERENTIAL GEOMETRY
Conference Name
Journal ISSN
0022-040X
1945-743X
1945-743X
Volume Title
98
Publisher
International Press of Boston