Needle decompositions and isoperimetric inequalities in Finsler geometry

• Ohta Shin-ichi

  Department of Mathematics Osaka University

抄録

Klartag recently gave a beautiful alternative proof of the isoperimetric inequalities of Lévy–Gromov, Bakry–Ledoux, Bayle and Milman on weighted Riemannian manifolds. Klartag's approach is based on a generalization of the localization method (so-called needle decompositions) in convex geometry, inspired also by optimal transport theory. Cavalletti and Mondino subsequently generalized the localization method, in a different way more directly along optimal transport theory, to essentially non-branching metric measure spaces satisfying the curvature-dimension condition. This class in particular includes reversible (absolutely homogeneous) Finsler manifolds. In this paper, we construct needle decompositions of non-reversible (only positively homogeneous) Finsler manifolds, and show an isoperimetric inequality under bounded reversibility constants. A discussion on the curvature-dimension condition CD(𝐾,𝑁) for 𝑁=0 is also included, it would be of independent interest.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 70 (2), 651-693, 2018

  一般社団法人 日本数学会

キーワード

• Finsler geometry
• Ricci curvature
• localization
• isoperimetric inequality

詳細情報

• CRID: 1390564237989617792
• NII論文ID: 130007383761
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/07027604
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 028962857
• Web Site: http://id.ndl.go.jp/bib/028962857
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I028962857
• 本文言語コード: en
• データソース種別:
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