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Mathematical Physics and Harmonic Analysis Seminar

Date: September 29, 2017

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Gerardo Mendoza, Temple University

  

Title: Free real actions, invariant CR structures, hypoellipticity, and Kodaira's vanishing theorem (joint with Several Complex Variables Seminar)

Abstract: Suppose M is a compact CR manifold with a nowhere vanishing real transverse vector field T that preserves the structure and admits an invariant metric which is Hermitian on the CR structure. Then -iT commutes with the Laplacians of the dee-bar complex and defines a selfadjoint operator on the kernel, H^q, of the Laplacian in each degree q with discrete spectrum without finite points of accumulation. Assuming non-degeneracy of the Levi form, we prove that only finitely many eigenvalues of -iT lie on the positive (or negative, depending on q and the signature of the Levi form) real axis. Finiteness of spectrum on one side or the other of 0 is strongly related to Kodaira's vanishing theorem.