Heat kernel asymptotics for Kohn Laplacians on CR manifolds

摘要

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. (c) 2022 Elsevier Inc. All rights reserved.