Convergence of Riemannian surfaces and convergence of the Bergman kernel

Bo-Yong Chen

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arXiv · 1507.01056

Convergence of Riemannian surfaces and convergence of the Bergman kernel

Bo-Yong Chen

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Abstract

Let $\{M_j\}$ be a sequence of complete Riemannian surfaces which converges in the sense of Cheeger-Gromov to a complete Riemannian surface $M$. We study the convergence of the Bergman kernel $K_{M_j}$ of $M_j$ by using isoperimetric inequalities.

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Bo-Yong Chen. 2015-07-04. Convergence of Riemannian surfaces and convergence of the Bergman kernel. https://arxiv.org/abs/1507.01056

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