Obstructions to the existence of limiting Carleman weights

2014/11/30 by Pablo Angulo-Ardoy, Daniel Faraco, Luis Guijarro +1 · 1 citation
Mathematics · #math.AP #msc:35R30 #msc:53A30

paper · pdf · doi:10.2140/apde.2016.9.575

published as Anal. PDE 9 (2016) 575-595 · Improved version

arxiv created 2015/06/10 · arxiv updated 2016/07/06

Abstract

We give a necessary condition for a Riemannian manifold to admit limiting Carleman weights in terms of the Weyl tensor (in dimensions 4 and higher) and the 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.

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