Heat kernel asymptotics for Kohn Laplacians on CR manifolds

Author(s)
Chin-Yu Hsiao, Weixia Zhu
Abstract

Let X be an abstract orientable (not necessarily compact) CR manifold of dimension 2n+1, n≥1, and let L

k be the k-th tensor power of a CR complex line bundle L over X. Suppose that condition Y(q) holds at each point of X, we establish asymptotics of the heat kernel of Kohn Laplacian with values in L

k. As an application, we give a heat kernel proof of Morse inequalities on compact CR manifolds. When X admits a transversal CR R-action, we also establish asymptotics of the R-equivariant heat kernel of Kohn Laplacian with values in L

k. As an application, we get R-equivariant Morse inequalities on compact CR manifolds with transversal CR R-action.

Organisation(s)
Department of Mathematics
External organisation(s)
Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt Road
Journal
Journal of Functional Analysis
Volume
284
ISSN
0022-1236
DOI
https://doi.org/10.1016/j.jfa.2022.109755
Publication date
11-2022
Peer reviewed
Yes
Austrian Fields of Science 2012
101008 Complex analysis
Keywords
ASJC Scopus subject areas
Analysis
Portal url
https://ucris.univie.ac.at/portal/en/publications/heat-kernel-asymptotics-for-kohn-laplacians-on-cr-manifolds(50d4ee60-e91c-427c-a6cd-0aab475d9c16).html