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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Published in	Manuscripta mathematica Vol. 171; no. 1-2; pp. 1 - 21
Main Author	Huang, Xian-Tao
Format	Journal Article
Language	English
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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Abstract	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.
AbstractList	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. 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.
Author	Huang, Xian-Tao
Author_xml	– sequence: 1 givenname: Xian-Tao surname: Huang fullname: Huang, Xian-Tao email: hxiant@mail2.sysu.edu.cn organization: School of Mathematics, Sun Yat-sen University
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Cites_doi	10.1016/j.na.2022.112839 10.1007/BF01388608 10.1007/s00222-018-0840-y 10.4007/annals.2009.169.903 10.1007/BF00252910 10.1007/s00222-016-0700-6 10.4171/JEMS/526 10.1007/BF02574061 10.1007/s00229-019-01138-5 10.1093/imrn/rny070 10.1090/memo/1180 10.1016/j.jfa.2019.06.016 10.1016/j.na.2013.12.008 10.1007/s00222-021-01040-6 10.2422/2036-2145.201906_012 10.3934/dcds.2016.36.303 10.1142/S021919971750081X 10.1016/j.na.2016.03.010 10.2140/apde.2020.13.2091 10.1007/BF01394058 10.1007/s00222-013-0452-5 10.1016/j.jfa.2010.03.024 10.1142/S0219199717500079 10.4171/CMH/110 10.1515/9783110550832-003 10.1007/s00220-013-1663-8 10.1007/s00526-022-02284-7 10.1007/s11511-006-0003-7 10.1007/s11511-006-0002-8
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Snippet	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... 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,...
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Title	Local isoperimetric inequalities in metric measure spaces verifying measure contraction property
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