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.
Citation
Bo-Yong Chen. Siqi Fu. "Stability of the Bergman kernel on a tower of coverings." J. Differential Geom. 104 (3) 371 - 398, November 2016. https://doi.org/10.4310/jdg/1478138546
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