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arXiv · 1011.2507

Nowhere conformally homogeneous manifolds and limiting Carleman weights

Tony Liimatainen·Mikko Salo
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Abstract

In this note we prove that a generic Riemannian manifold of dimension $\geq 3$ does not admit any nontrivial local conformal diffeomorphisms. This is a conformal analog of a result of Sunada concerning local isometries, and makes precise the principle that generic manifolds in high dimensions do not have conformal symmetries. Consequently, generic manifolds of dimension $\geq 3$ do not admit nontrivial conformal Killing vector fields near any point. As an application to the inverse problem of Calderón on manifolds, this implies that generic manifolds of dimension $\geq 3$ do not admit limiting Carleman weights near any point.

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Tony Liimatainen, Mikko Salo. 2010-11-10. Nowhere conformally homogeneous manifolds and limiting Carleman weights. https://arxiv.org/abs/1011.2507

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