Local isoperimetric inequalities in metric measure spaces verifying measure contraction property

We prove that on an essentially non-branching MCP ( K , N ) space, if a geodesic ball has a volume lower bound and satisfies some additional geometric conditions, then in a smaller geodesic ball (in a quantified sense) we have an estimate on the isoperimetric constants.

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Bibliographic Details
Published inManuscripta mathematica Vol. 171; no. 1-2; pp. 1 - 21
Main Author Huang, Xian-Tao
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2023
Springer Nature B.V
Subjects
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Differential geometry
Geometry
Lie Groups
Lower bounds
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
51Fxx
53C23
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Summary:We prove that on an essentially non-branching MCP ( K , N ) space, if a geodesic ball has a volume lower bound and satisfies some additional geometric conditions, then in a smaller geodesic ball (in a quantified sense) we have an estimate on the isoperimetric constants.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-022-01373-3