Heat kernel asymptotics for Kohn Laplacians on CR manifolds

2021/06/17 by Chin-Yu Hsiao, Hsiao, Chin-Yu, Weixia Zhu +1
Mathematics · #32G05 #32W05 #35J25 #35P15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2106.09268

openalex publication_date 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbb R-action, we also establish asymptotics of the \mathbb R-equivariant heat kernel of Kohn Laplacian with values in L^k. As an application, we get \mathbb R-equivariant Morse inequalities on compact CR manifolds with transversal CR \mathbb R-action.

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