We prove that if ( X, d, m) is an essentially non-branching metric measure space with m(X)=1, having Ricci curvature bounded from below by K and dimension bounded above by N ∈(1,∞) , understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality à la Lévy-Gromov holds true. Measure theoretic rigidity is also obtained.

Isoperimetric inequality under Measure-Contraction property / Cavalletti, Fabio; Santarcangelo, Flavia. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 277:9(2019), pp. 2893-2917. [10.1016/j.jfa.2019.06.016]

Isoperimetric inequality under Measure-Contraction property

Cavalletti, Fabio;Santarcangelo, Flavia
2019

Abstract

We prove that if ( X, d, m) is an essentially non-branching metric measure space with m(X)=1, having Ricci curvature bounded from below by K and dimension bounded above by N ∈(1,∞) , understood as a synthetic condition called Measure-Contraction property, then a sharp isoperimetric inequality à la Lévy-Gromov holds true. Measure theoretic rigidity is also obtained.
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https://arxiv.org/abs/1810.11289
Cavalletti, Fabio; Santarcangelo, Flavia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/95501
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