A Closed Formula for the Asymptotic Expansion of the Bergman Kernel

作者：Xu Hao^*

来源：Communications in Mathematical Physics, 2012, 314(3): 555-585.

DOI：10.1007/s00220-012-1531-y

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 and A. Loi.

• 出版日期2012-9