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://ucrisportal.univie.ac.at/en/publications/50d4ee60-e91c-427c-a6cd-0aab475d9c16