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. 2020 Mathematics Subject Classification: 53C23, 51Fxx.

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