2024 / June Volume 19 No.2
$L^2$-estimates for the Dirac-Dolbeault operator and Bergman kernel asymptotics on some classes of non-compact complex manifolds
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2024 / June
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Title | $L^2$-estimates for the Dirac-Dolbeault operator and Bergman kernel asymptotics on some classes of non-compact complex manifolds |
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Pagination | 139-180 |
Abstract | For high power $k$, the $L^2$-estimates for the Dirac-Dolbeault operator with coefficient $L^k\otimes E$ can be obtained from the Bochner-Kodaira-Nakano identity if $L$ has positive curvature. In this article, we generalize the classical method to obtain $L^2$-estimates for mixed curvature case, and give a bound to the extra error term. Modifying the $L^2$-estimates and existence theorems for $\bar{\partial}$-operator, we can get a local spectral gap of the Kodaira Laplacian $\Box$ and thus a full asymptotic expansion for Bergman kernel. |
DOI | |
AMS Subject Classification |
32L10
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Received |
2023-10-24
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