$L^2$-estimates for the Dirac-Dolbeault operator and Bergman kernel asymptotics on some classes of non-compact complex manifolds
Year: 2024
Type: article
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.
Author: Chang Ming-Yuan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4401190342