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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Mots clés : Bergman kernels
@article{AFST_2020_6_29_4_795_0,
author = {Aryasomayajula, Anilatmaja and Majumder, Priyanka},
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 = {http://www.numdam.org/articles/10.5802/afst.1646/}
}
TY - JOUR AU - Aryasomayajula, Anilatmaja AU - Majumder, Priyanka TI - Estimates of the Bergman kernel on a hyperbolic Riemann surface of finite volume-II JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 795 EP - 804 VL - 29 IS - 4 PB - Université Paul Sabatier, Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1646/ DO - 10.5802/afst.1646 LA - en ID - AFST_2020_6_29_4_795_0 ER -
%0 Journal Article %A Aryasomayajula, Anilatmaja %A Majumder, Priyanka %T Estimates of the Bergman kernel on a hyperbolic Riemann surface of finite volume-II %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 795-804 %V 29 %N 4 %I Université Paul Sabatier, Toulouse %U http://www.numdam.org/articles/10.5802/afst.1646/ %R 10.5802/afst.1646 %G en %F AFST_2020_6_29_4_795_0
Aryasomayajula, Anilatmaja; Majumder, Priyanka. 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. http://www.numdam.org/articles/10.5802/afst.1646/
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