Bergman kernels on punctured Riemann surfaces - Kölner UniversitätsPublikationsServer

Auvray, Hugues, Ma, Xiaonan ORCID: 0000-0001-8960-7623 and Marinescu, George ORCID: 0000-0001-6539-7860 . Bergman kernels on punctured Riemann surfaces. Math. Ann.. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1807

Full text not available from this repository.

DOI:10.1007/s00208-020-01957-y

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. One of the technical tools is a new weighted elliptic estimate near the punctures, which is uniform with respect to the tensor power. As a consequence, we obtain an optimal uniform estimate of the supremum norm of the Bergman kernel, involving a fractional growth order of the tensor power. This holds in particular for the Bergman kernel of cusp forms of high weight of non-cocompact geometrically finite Fuchsian groups of first kind without elliptic elements.

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