On the set of metrics without local limiting Carleman weights

Pablo Angulo-Ardoy

doi:10.3934/ipi.2017003

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2017, Volume 11, Issue 1: 47-64. Doi: 10.3934/ipi.2017003

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On the set of metrics without local limiting Carleman weights

Pablo Angulo-Ardoy

E.T.S de Ingenieros Navales, Universidad Politécnica de Madrid, Avd. Arco de la Victoria, No4, Ciudad Universitaria Madrid -28040, Spain

Received: July 2015

Revised: November 2016

Published online: January 2017

The author was supported by research grant ERC 301179

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Abstract

In the paper [1] it is shown that the set of Riemannian metrics which do not admit global limiting Carleman weights is open and dense, by studying the conformally invariant Weyl and Cotton tensors. In the paper [7] it is shown that the set of Riemannian metrics which do not admit local limiting Carleman weights at any point is residual, showing that it contains the set of metrics for which there are no local conformal diffeomorphisms between any distinct open subsets. This paper is a continuation of [1], in order to prove that the set of Riemannian metrics which do not admit local limiting Carleman weights at any point is open and dense.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 53A30.

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References

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