Green functions and conformal geometry.
type: Item
instance of: scholarly article
title: Green functions and conformal geometry.
zbMATH Open document ID: 1071.53023
author: Lutz Habermann
author: Jürgen Jost
published in: Journal of Differential Geometry
publication date: 2002-08-15T00:00:00Z
full work available at URL: 3 1.pdf
review text: A canonical metric, which is unique in its conformal class is constructed here with the Green function of the Yamabe operator (conformal Laplacian) and used for investigating the moduli space of locally conformally flat structures. This construction depends on the positive mass theorem of Schoen-Yau and the resulting metric is different from those obtained earlier by other methods. The behavior of the canonical metric under surgery-type degeneration is analyzed and the main result says that the limit of the canonical metrics yields the canonical metric of the limit space. Consequently, the \(L^2\)-metric on the moduli space of scalar positive locally conformally flat structures is not complete and the example of \(S^1 \times S^2\) as underlying manifold is studied.
reviewed by: Cornelia-Livia Bejan
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 1782628
zbMATH Keywords: Green function
zbMATH Keywords: conformal geometry
zbMATH Keywords: Yamabe operator
MaRDI profile type: Publication
OpenAlex ID: W1526233120
Wikidata QID: Q115193449
DOI: 10.4310/JDG/1214425634
description: scientific article; zbMATH DE number 1782628