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Obstructions to the
existence of limiting Carleman weights
Pablo Angulo-Ardoy, Daniel Faraco, Luis Guijarro and Alberto Ruiz |
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Vol. 9 (2016), No. 3, 575–595
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 35R30, 53A30
Secondary: 58J32
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Milestones
Received: 10 September 2014
Revised: 15 June 2015
Accepted: 30 January 2016
Published: 17 June 2016
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Authors |
| Pablo Angulo-Ardoy | |
| Department of Mathematics Universidad Autónoma de Madrid 28049 Madrid Spain |
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| 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 |
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