Estimates of the Bergman kernel on a hyperbolic Riemann surface of finite volume-II
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 4, pp. 795-804.

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

Dans cet article, nous dérivons des estimations non-diagonales du noyau de Bergman associé aux puissances tensorielles du faisceau cotangent défini sur une surface de Riemann hyperbolique de volume fini, lorsque la distance entre les points est inférieure au rayon d’injectivité. Nous utilisons ensuite ces estimations pour dériver des estimations du noyau de Bergman le long de la diagonale.

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DOI: 10.5802/afst.1646
Classification: 32A25, 30F30, 30F35
Keywords: Bergman kernels

Anilatmaja Aryasomayajula 1; Priyanka Majumder 1

1 Department of Mathematics, Indian Institute of Science Education and Research Tirupati, Tirupati-517507 (India)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Anilatmaja Aryasomayajula; Priyanka Majumder. Estimates of the Bergman kernel on a hyperbolic Riemann surface of finite volume-II. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 4, pp. 795-804. doi : 10.5802/afst.1646. https://afst.centre-mersenne.org/articles/10.5802/afst.1646/

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