Aubin's lemma for the Yamabe constants of infinite coverings and a positive mass theorem
type: Item
instance of: scholarly article
title: Aubin's lemma for the Yamabe constants of infinite coverings and a positive mass theorem
zbMATH Open document ID: 1239.53045
author: Kazuo Akutagawa
published in: Mathematische Annalen
publication date: 2012-04-04T00:00:00Z
review text: A generalization of Aubin's lemma for the Yamabe constant of infinite conformal coverings \((M_\infty ,C_\infty)\) of a closed positive conformal manifold \((M,C)\) is proved, under the condition that \(\pi_1(M)\) has a descending chain of finite index subgroups tending to \(\pi_1(M_\infty)\). A version of positive mass theorem for a specific class of asymptotically flat manifolds with singularities is established. This is used to prove that if the covering \(M_\infty\) is normal, then the limit of the Yamabe constants of the finite conformal coverings associated to the descending chain is equal to that of \((M_\infty ,C_\infty)\).
reviewed by: Gheorghe Pitiş
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 6021950
zbMATH Keywords: conformal manifold
zbMATH Keywords: conformal covering
zbMATH Keywords: Yamabe invariant
zbMATH Keywords: Aubin lemma
MaRDI profile type: Publication
full work available at URL: s00208-011-0667-y
OpenAlex ID: W1994856510
Wikidata QID: Q124982577
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DOI: 10.1007/S00208-011-0667-Y
description: scientific article; zbMATH DE number 6021950