Skip to main content
Download PDF
- Main
On the Spectrum of Laplace Operator and Asymptotic Expansion of Bergman Kernel on Kähler Manifolds
- Xu, Hang
- Advisor(s): Lu, Zhiqin
Abstract
This dissertation contains two parts. The first part considers related problems of Laplace operator on Kähler manifolds. Together with my advisor Zhiqin Lu, we generalized the spectrum relation in [5] to any Hermitian manifolds. And we proved the closure of Laplace operator on the moduli space of polarized Calabi-Yau manifolds is self-adjoint. The second part considers the asymptotic expansion of the Bergman kernel on a polarized Kähler manifold. Together with Hezari, Kelleher and Seto [9], we give an alternative proof of the asymptotic expansion.