NOWHERE CONFORMALLY HOMOGENEOUS MANIFOLDS AND LIMITING CARLEMAN WEIGHTS

作者：Liimatainen Tony^*; Salo Mikko

来源：Inverse Problems and Imaging, 2012, 6(3): 523-530.

DOI：10.3934/ipi.2012.6.523

• Carleman weight
• conformal Killing vector
• Sunada%26apos
• s lemma

In this note we prove that a generic Riemannian manifold of dimension %26gt;= 3 does not admit any nontrivial local conformal diffeomorphisms. This is a conformal analogue 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 %26gt;= 3 do not admit nontrivial conformal Killing vector fields near any point. As an application to the inverse problem of Calderon on manifolds, this implies that generic manifolds of dimension %26gt;= 3 do not admit limiting Carleman weights near any point.

• 出版日期2012-8