2016/03/14 by Pablo Angulo-Ardoy, Daniel Faraco, Angulo-Ardoy, Pablo +3
Mathematics · #35R30 #53A30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35R30 #msc:53A30
paper · pdf · doi:10.48550/arxiv.1603.04201
arxiv created 2016/03/14 · arxiv updated 2016/03/15
In https://arxiv.org/abs/1411.4887, we found some necessary conditions for a Riemannian manifold to admit a local limiting Carleman weight (LCW), based upon the Cotton-York tensor in dimension 3 and the Weyl tensor in dimension 4. In this paper, we find further necessary conditions for the existence of local LCWs that are often sufficient. For a manifold of dimension 3 or 4, we classify the possible Cotton-York, or Weyl tensors, and provide a mechanism to find out whether the manifold admits local LCW for each type of tensor. In particular, we show that a product of two surfaces admits a LCW if and only if at least one of the two surfaces is of revolution. This provides an example of a manifold satisfying the eigenflag condition of \citeAFGR but not admitting LCW.