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

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.

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.

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DOI : https://doi.org/10.5802/afst.1646
Classification : 32A25,  30F30,  30F35
Mots clés : Bergman kernels
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     author = {Anilatmaja Aryasomayajula and Priyanka Majumder},
     title = {Estimates of the {Bergman} kernel on a hyperbolic {Riemann} surface of finite {volume-II}},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {795--804},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {4},
     year = {2020},
     doi = {10.5802/afst.1646},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1646/}
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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, Série 6, Tome 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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