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• W3173443669 abstract "The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by J. Lott, K.-T. Sturm and C. Villani, the noncompact case provides various surprising phenomena. Since the reversibility of noncompact irreversible spaces might be infinite, it is motivated to introduce a suitable nondecreasing function that bounds the reversibility of larger and larger balls. By this approach, we are able to prove satisfactory convergence/stability results in a suitable -- reversibility depending -- Gromov-Hausdorff topology. A wide class of irreversible spaces is provided by Finsler manifolds, which serve to construct various model examples by pointing out genuine differences between the reversible and irreversible settings. We conclude the paper by proving various geometric and functional inequalities (as Brunn-Minkowski, Bishop-Gromov, log-Sobolev and Lichnerowicz inequalities) on irreversible structures." @default.
• W3173443669 created "2021-07-05" @default.
• W3173443669 creator A5054380581 @default.
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• W3173443669 date "2021-06-25" @default.
• W3173443669 modified "2023-09-27" @default.
• W3173443669 title "On the geometry of irreversible metric-measure spaces: Convergence, Stability and Analytic aspects" @default.
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• W3173443669 doi "https://doi.org/10.48550/arxiv.2106.13609" @default.
• W3173443669 hasPublicationYear "2021" @default.
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