Vol. 9, No. 3, 2016

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Obstructions to the existence of limiting Carleman weights

Pablo Angulo-Ardoy, Daniel Faraco, Luis Guijarro and Alberto Ruiz

Vol. 9 (2016), No. 3, 575–595
Abstract

We give a necessary condition for a Riemannian manifold to admit limiting Carleman weights in terms of its Weyl tensor (in dimensions 4 and higher), or its Cotton–York tensor in dimension 3. As an application, we provide explicit examples of manifolds without limiting Carleman weights and show that the set of such metrics on a given manifold contains an open and dense set.

Keywords
Calderón problem, limiting Carleman weights, conformal geometry, Cotton–York tensor, Weyl tensor, conformal to a product
Mathematical Subject Classification 2010
Primary: 35R30, 53A30
Secondary: 58J32
Milestones
Received: 10 September 2014
Revised: 15 June 2015
Accepted: 30 January 2016
Published: 17 June 2016
Authors
Pablo Angulo-Ardoy
Department of Mathematics
Universidad Autónoma de Madrid
28049 Madrid
Spain
Daniel Faraco
Department of Mathematics
Universidad Autónoma de Madrid
28049 Madrid
Spain
Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UC3M
28049 Madrid
Spain
Luis Guijarro
Department of Mathematics
Universidad Autónoma de Madrid
28049 Madrid
Spain
Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UC3M
28049 Madrid
Spain
Alberto Ruiz
Department of Mathematics
Universidad Autónoma de Madrid
28049 Madrid
Spain
Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UC3M
28049 Madrid
Spain