香蕉视频

Title: Zero and negative eigenvalues of conformally covariant operators, and nodal sets in conformal geometry

Abstract: We first review some old results about conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, as well as applications to curvature prescription problems. Next, we discuss related results on manifolds with boundary. We relate Dirichlet and Neumann eigenvalues for conformally covariant boundary value problems. If time permits, we shall discuss related results for boundary operators of arbitrary order, as well as for weighted graphs. This is joint work with Y. Canzani, R. Gover, R. Ponge, A. Hassannezhad, M. Levitin, M. Karpukhin, G. Cox and Y. Sire.