On the singularities of the Bergman projections for lower energy forms on complex manifolds with boundary

2019/11/25 by Chin-Yu Hsiao, Hsiao, Chin-Yu, George Marinescu +1
Mathematics · #Holomorphic and Operator Theory #Geometry and complex manifolds #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1911.10928

Abstract

Let M be a complex manifold of dimension n with smooth boundary X. Given q∈\0,1,…,n-1\, let \Box^(q) be the \ddbar-Neumann Laplacian for (0,q) forms. We show that the spectral kernel of \Box^(q) admits a full asymptotic expansion near the non-degenerate part of the boundary X and the Bergman projection admits an asymptotic expansion under some local closed range condition. As applications, we establish Bergman kernel asymptotic expansions for some domains with weakly pseudoconvex boundary and S¹-equivariant Bergman kernel asymptotic expansions and embedding theorems for domains with holomorphic S¹-action.

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