Local isoperimetric inequalities in metric measure spaces verifying measure contraction property

DOI10.1007/S00229-022-01373-3zbMATH Open1514.53084arXiv2109.07530MaRDI QIDQ6377769

Xian-Tao Huang

Publication date: 15 September 2021

Abstract: We prove that on an essentially non-branching $mathrmMCP(K,N)$ 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.

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Length, area, volume, other geometric measure theory (28A75) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Inequalities and extremum problems in real or complex geometry (51M16)

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