Convergence speed of weighted Bergman kernels towards extremal functions

2017/05/22 by Guokuan Shao, Shao, Guokuan
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV

paper · pdf · doi:10.48550/arxiv.1705.07656

11 pages

arxiv created 2017/05/22 · openalex publication_date 2017/05/22 · arxiv updated 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct inner products by the Bernstein-Markov inequality on spaces of holomorphic sections of high powers of a line bundle. The corresponding weighted Bergman kernel functions converge to an extremal function. We obtain a uniform convergence speed.

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