\(L^2\) harmonic forms on some complete Kähler manifolds
type: Item
instance of: scholarly article
title: \(L^2\) harmonic forms on some complete Kähler manifolds
zbMATH Open document ID: 1013.32016
published in: Mathematische Annalen
publication date: 2002-09-17T00:00:00Z
review text: The goal of this paper is to obtain vanishing theorems for \(H^{p,q}_{(2)} (M),\) the space of \(L^{2}\) harmonic \((p,q)\) forms, for \( p+q\) not equal to the middle dimension \(n.\) This is accomplished under the assumption that the metric potential \( \lambda\) ``dominate its gradient'', a boundedness condition which is defined in the paper and which is reminiscent of Gromov's notion of Kähler hyperbolicity. An application is made to the Cauchy-Riemann equation \(\overline{\partial } u = \alpha ,\) and examples are given.
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 1801554
zbMATH Keywords: \(L^{2}\) cohomology
zbMATH Keywords: vanishing theorems
zbMATH Keywords: space of \(L^{2}\) harmonic \((p,q)\) forms
zbMATH Keywords: Kähler hyperbolicity
author: J. D. McNeal
reviewed by: Thalia Jeffres
MaRDI profile type: Publication
full work available at URL: s002080100305
OpenAlex ID: W2019871945
DOI: 10.1007/S002080100305
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description: scientific article; zbMATH DE number 1801554