Inverse scattering with partial data on asymptotically hyperbolic manifolds

Hora, Raphael; Barreto, Antônio

doi:10.2140/apde.2015.8.513

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Inverse scattering with partial data on asymptotically hyperbolic manifolds

Raphael Hora and Antônio Sá Barreto

Vol. 8 (2015), No. 3, 513–559

DOI: 10.2140/apde.2015.8.513

Abstract

We prove a local support theorem for the radiation fields on asymptotically hyperbolic manifolds and use it to show that the scattering operator restricted to an open subset of the boundary of the manifold determines the manifold and the metric modulo isometries that are equal to the identity on the open subset where the scattering operator is known.

Keywords

inverse scattering, asymptotically hyperbolic manifolds

Mathematical Subject Classification 2010

Primary: 35P25, 58J50

Milestones

Received: 3 September 2013

Revised: 23 December 2014

Accepted: 22 January 2015

Published: 3 June 2015

Authors

Raphael Hora
Departamento de Matemática Universidade Federal de Santa Catarina Campus Universitário Trindade 88040-900 Florianópolis, SC Brazil

Antônio Sá Barreto
Department of Mathematics Purdue University 150 North University Street West Lafayette, IN 47907 United States

Vol. 8, No. 3, 2015