Asian Journal of Mathematics

Volume 20 (2016)

Number 1

Lens rigidity with trapped geodesics in two dimensions

Pages: 47 – 58

DOI: https://dx.doi.org/10.4310/AJM.2016.v20.n1.a3

Authors

Christopher B. Croke (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Pilar Herreros (Departamento de Matemática, Pontificia Universidad Católica de Chile, Santiago, Chile)

Abstract

We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat Möbius strip are determined by their lens data. We also see by example that the flat Möbius strip is not determined by it’s scattering data. We then consider the case of negatively curved cylinders with convex boundary and show that they are lens rigid.

Keywords

scattering rigidity, lens rigidity, trapped geodesics

2010 Mathematics Subject Classification

53C22, 53C24

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Published 28 January 2016