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On the singularities
of the spectral and Bergman projections on complex manifolds
with boundary
Chin-Yu Hsiao and George Marinescu |
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Vol. 18 (2025), No. 2, 409–474
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Abstract |
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We show that the spectral kernel of the -Neumann Laplacian acting on -forms on a smooth relatively compact domain admits a full asymptotic expansion near the nondegenerate part of the boundary. We show further that the Bergman projection admits an asymptotic expansion under certain local closed range condition. In particular, if condition fails but conditions and hold, the Bergman projection on -forms admits an asymptotic expansion. As applications, we establish Bergman kernel asymptotic expansions near nondegenerate points of some domains with weakly pseudoconvex boundary and -equivariant asymptotic expansions and embedding theorems for domains with holomorphic -action. |
Keywords
Bergman kernel, $\bar\partial$-Neumann problem, Fourier
integral operator with complex phase
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Mathematical Subject Classification
Primary: 32A25, 32L05, 58J50
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Milestones
Received: 3 November 2022
Revised: 4 September 2023
Accepted: 6 November 2023
Published: 5 February 2025
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Authors |
| Chin-Yu Hsiao | |
| Department of Mathematics National Taiwan University Taipei Taiwan |
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| George Marinescu | |
| Department of Mathematics and
Computer Science Universität zu Köln Köln Germany |
Institute of Mathematics “Simion
Stoilow” Romanian Academy Bucharest Romania |
| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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