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A closed formula for the asymptotic expansion of the Bergman kernel

Hao Xu University of Pittsburgh

Differential Geometry mathscidoc:1704.10001

Distinguished Paper Award in 2017

Comm. Math. Phys., 314, 2012
We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formula due to M. Engli\v s and A. Loi.
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@inproceedings{hao2012a,
  title={A closed formula for the asymptotic expansion of the Bergman kernel},
  author={Hao Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170404231730950620738},
  booktitle={Comm. Math. Phys.},
  volume={314},
  year={2012},
}
Hao Xu. A closed formula for the asymptotic expansion of the Bergman kernel. 2012. Vol. 314. In Comm. Math. Phys.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170404231730950620738.
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