Communications in Analysis and Geometry

Volume 25 (2017)

Number 5

Invariant distributions and tensor tomography for Gaussian thermostats

Pages: 895 – 926

DOI: http://dx.doi.org/10.4310/CAG.2017.v25.n5.a1

Authors

Yernat M. Assylbekov (Department of Mathematics, University of Washington, Seattle, Wa., U.S.A.; and Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.)

Hanming Zhou (Department of Mathematics, University of Washington, Seattle, Wa., U.S.A.; and Department of Mathematics, University of California at Santa Barbara)

Abstract

In this paper we consider the Gaussian thermostat ray transforms on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the surjectivity of its adjoint.

2010 Mathematics Subject Classification

35R30, 53C65

Full Text (PDF format)

The authors want to thank their PhD advisor, Professor Gunther Uhlmann, for all his support and encouragement. Thanks are also due to Professor Gabriel Paternain and Professor Mikko Salo for helpful discussions and sharing their knowledges on the topics. The authors are also grateful to the referees for helpful comments and suggestions. The work was partially supported by NSF.

Received 7 November 2014

Published 30 November 2017