Let be a bounded domain with the hyperconvexity index . Let be the relative extremal function of a fixed closed ball in , and set and . We obtain the following estimates for the Bergman kernel. (1) For every and , there exists a constant such that for all . (2) For every , there exists a constant such that for all . Various applications of these estimates are given.
"Bergman kernel and hyperconvexity index." Anal. PDE 10 (6) 1429 - 1454, 2017. https://doi.org/10.2140/apde.2017.10.1429