## Journal of Differential Geometry

### Stability of the Bergman kernel on a tower of coverings

#### Abstract

We obtain several results about stability of the Bergman kernel on a tower of coverings on complex manifolds. An effective estimate for stability of the Bergman kernel is given for a tower of coverings on a compact Riemann surface of genus $\geq 2$. Stability of the Bergman kernel is established for towers of coverings on all hyperbolic Riemann surfaces and on complete Kähler manifolds that satisfy certain potential conditions. As a consequence, stability of the Bergman kernel is established for any tower of coverings of Riemann surfaces.

#### Article information

Source
J. Differential Geom., Volume 104, Number 3 (2016), 371-398.

Dates
First available in Project Euclid: 3 November 2016

https://projecteuclid.org/euclid.jdg/1478138546

Digital Object Identifier
doi:10.4310/jdg/1478138546

Mathematical Reviews number (MathSciNet)
MR3568625

Zentralblatt MATH identifier
1360.32003

#### Citation

Chen, Bo-Yong; Fu, Siqi. Stability of the Bergman kernel on a tower of coverings. J. Differential Geom. 104 (2016), no. 3, 371--398. doi:10.4310/jdg/1478138546. https://projecteuclid.org/euclid.jdg/1478138546