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Local isoperimetric inequalities in metric measure spaces verifying measure contraction property

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Abstract

We prove that on an essentially non-branching \(\mathrm {MCP}(K,N)\) 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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Acknowledgements

The author would like to thank Prof. X.-P. Zhu, H.-C. Zhang and B.-X. Han for discussions. The author would like to thank the anonymous referees for careful reading and giving helpful suggestions. The author is partially supported by NSFC (Nos. 12025109 and 11521101) and Guang-dong Natural Science Foundation 2019A1515011804.

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  1. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Xian-Tao Huang

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Huang, XT. Local isoperimetric inequalities in metric measure spaces verifying measure contraction property. manuscripta math. 171, 1–21 (2023). https://doi.org/10.1007/s00229-022-01373-3

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  • DOI: https://doi.org/10.1007/s00229-022-01373-3

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