Mathematical Research Letters

Volume 27 (2020)

Number 3

Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials

Pages: 743 – 787



Hamid Hezari (Department of Mathematics, University of California at Irvine)

Hang Xu (Department of Mathematics, Johns Hopkins University, Baltimore, Maryland, U.S.A.)


We prove upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.

Received 1 August 2018

Accepted 23 September 2018

Published 20 August 2020