Communications in Analysis and Geometry

Volume 31 (2023)

Number 2

Bergman functions and the equivalence problem of singular domains

Pages: 449 – 483



Bingyi Chen (Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Stephen S.-T. Yau (Department of Mathematical Sciences, Tsinghua University, Beijing, China; and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China)


In this article, we use the Bergman function, which is introduced by the second author in $\href{}{[\textrm{Ya}]}$, to study the equivalence problem of bounded complete Reinhardt domains in the singular variety $\widetilde{V} = \lbrace (u_1, u_2, u_3, u_4) \in \mathbb{C}^4 \vert u_1 u_4 = u_2 u_3 \rbrace$.

The second author is supported by NSFC Grant (11531007), Tsinghua University start-up fund as well as Tsinghua University Education Foundation fund (042202008).

Received 27 June 2020

Accepted 23 September 2020

Published 6 December 2023