Uniform Boundedness on Extremal Subsets in Alexandrov Spaces

Fujioka, Tadashi

doi:https://doi.org/10.1007/s12220-024-01864-7

Uniform Boundedness on Extremal Subsets in Alexandrov Spaces

Fujioka, Tadashi

Journal of Geometric Analysis, 2025, 35, 46

アクセス数:54件（2026-02-16 01:32 集計）

固定URL: https://hdl.handle.net/11094/100132

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タイトル	Uniform Boundedness on Extremal Subsets in Alexandrov Spaces
著者	ORCID 0000-0002-3628-4338 0000-0002-3628-4338 researchmap permalink tadashifujioka tadashifujioka 著者名 Fujioka, Tadashi
キーワード等	Alexandrov spaces
	Betti numbers
	Collapse
	Essential coverings
	Extremal subsets
	Volume
内容	The version of record of this article, first published in Journal of Geometric Analysis, is available online at Publisher’s website: https://doi.org/10.1007/s12220-024-01864-7.
抄録	In this paper, we study extremal subsets in Alexandrov spaces with dimension n, curvature ≥κ, and diameter ≤D. We show that the following three quantities are uniformly bounded above in terms of n, κ, and D: (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal subset; (3) the volume of an extremal subset. The proof is an application of essential coverings introduced by Yamaguchi.
出版者	Springer
収録物名	Journal of Geometric Analysis
巻(号)	35
ページ	46
刊行年月	2025-02-01
言語	英語
ハンドルURL	https://hdl.handle.net/11094/100132
PISSN	10506926
関連情報 (isIdenticalTo)	DOI (出版社版) https://doi.org/10.1007/s12220-024-01864-7
アクセス権	open access
権利情報	This article is licensed under a Creative Commons Attribution 4.0 International License.
出版タイプ	Version of Record
カテゴリ	学術雑誌論文 Journal Article

資源タイプ	学術雑誌論文
ローカル資源タイプ	学術雑誌論文
DCTERMS.bibliographicCitation	Journal of Geometric Analysis. 2025, 35, p. 46
DC.title	Uniform Boundedness on Extremal Subsets in Alexandrov Spaces
DC.creator	Fujioka, Tadashi
DC.publisher	Springer
DC.language' scheme='DCTERMS.RFC1766	英語
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2025-02-01
DC.identifier	https://doi.org/10.1007/s12220-024-01864-7
DC.subject	Alexandrov spaces
	Betti numbers
	Collapse
	Essential coverings
	Extremal subsets
	Volume
DC.description	The version of record of this article, first published in Journal of Geometric Analysis, is available online at Publisher’s website: https://doi.org/10.1007/s12220-024-01864-7.
DCTERMS.abstract	In this paper, we study extremal subsets in Alexandrov spaces with dimension n, curvature ≥κ, and diameter ≤D. We show that the following three quantities are uniformly bounded above in terms of n, κ, and D: (1) the number of extremal subsets in an Alexandrov space; (2) the Betti numbers of an extremal subset; (3) the volume of an extremal subset. The proof is an application of essential coverings introduced by Yamaguchi.
DC.rights	This article is licensed under a Creative Commons Attribution 4.0 International License.
DC.format	100132
citation_title	Uniform Boundedness on Extremal Subsets in Alexandrov Spaces
citation_author	Fujioka, Tadashi
citation_publisher	Springer
citation_language	英語
citation_date	2025-02-01
citation_journal_title	Journal of Geometric Analysis
citation_volume	35
citation_firstpage	46
citation_doi	https://doi.org/10.1007/s12220-024-01864-7
citation_public_url	https://hdl.handle.net/11094/100132

Uniform Boundedness on Extremal Subsets in Alexandrov Spaces

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