EVOLUTION OF RELATIVE YAMABE CONSTANT UNDER RICCI FLOW

Botvinnik, Boris; Lu, Peng

doi:https://doi.org/10.18910/76680

EVOLUTION OF RELATIVE YAMABE CONSTANT UNDER RICCI FLOW

Botvinnik, Boris; Lu, Peng

Osaka Journal of Mathematics, 2020, 57(3), 679-687

アクセス数:111件（2025-07-01 06:49 集計）

固定URL: https://doi.org/10.18910/76680

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タイトル	EVOLUTION OF RELATIVE YAMABE CONSTANT UNDER RICCI FLOW
著者	著者名 Botvinnik, Boris
著者	著者名 Lu, Peng
抄録	Let W be a manifold with boundary M given together with a conformal class C^^－ which restricts to a conformal class C on M. Then the relative Yamabe constant Y_ C^^－ (W, M;C) is well-defined. We study the short-time behavior of the relative Yamabe constant Y_[g^^－t ](W, M;C) under the Ricciflow g^^－t on W with boundary conditions that mean curvature Hg^^－t ≡ 0 and g^^－t\|M ∈ C = [g^^－0]. In particular, we show that if the initial metric g^^－0 is a Yamabe metric, then, under some natural assumptions, d/dt _<t=0> Y_[g^^－t ](W, M;C) ≥ 0 and is equal to zero if and only the metric g^^－0 is Einstein.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	57(3)
ページ	679-687
刊行年月	2020-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/76680
DOI	https://doi.org/10.18910/76680
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 57, Number 3 （2020-7）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2020, 57(3), p. 679-687
DC.title	EVOLUTION OF RELATIVE YAMABE CONSTANT UNDER RICCI FLOW
DC.creator	Botvinnik, Boris
DC.creator	Lu, Peng
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2020-07
DCTERMS.abstract	Let W be a manifold with boundary M given together with a conformal class C^^－ which restricts to a conformal class C on M. Then the relative Yamabe constant Y_ C^^－ (W, M;C) is well-defined. We study the short-time behavior of the relative Yamabe constant Y_[g^^－t ](W, M;C) under the Ricciflow g^^－t on W with boundary conditions that mean curvature Hg^^－t ≡ 0 and g^^－t\|M ∈ C = [g^^－0]. In particular, we show that if the initial metric g^^－0 is a Yamabe metric, then, under some natural assumptions, d/dt _<t=0> Y_[g^^－t ](W, M;C) ≥ 0 and is equal to zero if and only the metric g^^－0 is Einstein.
DC.identifier	10.18910/76680
DC.format	76680
citation_title	EVOLUTION OF RELATIVE YAMABE CONSTANT UNDER RICCI FLOW
citation_author	Botvinnik, Boris
citation_author	Lu, Peng
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2020-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	57
citation_issue	3
citation_firstpage	679
citation_lastpage	687
citation_public_url	https://hdl.handle.net/11094/76680
citation_doi_detail	10.18910/76680
citation_doi	https://doi.org/10.18910/76680

EVOLUTION OF RELATIVE YAMABE CONSTANT UNDER RICCI FLOW

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