Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials

2018/06/30 by Hamid Hezari, Hang Xu, Hezari, Hamid +1
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1807.00204

openalex publication_date 2018/06/30 · openalex created_date 2018/07/10 · openalex updated_date 2026/07/28

Abstract

We give 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.

Related

• Asymptotic properties of Bergman kernels for potentials with Gevrey regularity
• Off-diagonal asymptotic properties of Bergman kernels associated to analytic Kähler potentials
• Asymptotic expansion of the Bergman kernel via perturbation of the Bargmann-Fock model
• Asymptotics of Bergman kernels
• Off-diagonal decay of Bergman kernels: On a conjecture of Zelditch