Estimates of the Bergman kernel on a hyperbolic Riemann surface of\n finite volume-II

2018/08/14 by Anilatmaja Aryasomayajula, Aryasomayajula, Anilatmaja, Priyanka Majumder +1 · 1 citation
Mathematics · #30F30 #30F35 #32A25 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1808.04646

openalex publication_date 2018/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we derive off-diagonal estimates of the Bergman kernel\nassociated to the tensor-powers of the cotangent bundle defined on a hyperbolic\nRiemann surface of finite volume, when the distance between the points is less\nthan injectivity radius. We then use these estimates to derive estimates of the\nBergman kernel along the diagonal.\n

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• Off-diagonal estimates of the Bergman kernel associated to Siegel varieties

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