Universität zu Köln

Auvray, Hugues, Ma, Xiaonan ORCID: 0000-0001-8960-7623 and Marinescu, George ORCID: 0000-0001-6539-7860 (2016). Bergman kernels on punctured Riemann surfaces. C. R. Math., 354 (10). S. 1018 - 1023. PARIS: ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER. ISSN 1778-3569

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Abstract

In this paper, we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincare metric near the punctures and a holomorphic line bundle that polarizes the metric. We show that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the punctured unit disc endowed with the standard Poincare metric. As a consequence, we obtain an optimal uniform estimate of the supremum norm of the Bergman kernel function, involving a fractional growth order of the tensor power. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Auvray, Hugues UNSPECIFIED UNSPECIFIED UNSPECIFIED Ma, Xiaonan UNSPECIFIED orcid.org/0000-0001-8960-7623 UNSPECIFIED Marinescu, George UNSPECIFIED orcid.org/0000-0001-6539-7860 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-260361
DOI:	10.1016/j.crma.2016.08.006
Journal or Publication Title:	C. R. Math.
Volume:	354
Number:	10
Page Range:	S. 1018 - 1023
Date:	2016
Publisher:	ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
Place of Publication:	PARIS
ISSN:	1778-3569
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language METRICS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/26036