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On the geometry of irreversible metric-measure spaces: Convergence, stability and analytic aspects
- Source :
- Journal de Mathématiques Pures et Appliquées. 158:216-292
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
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.
- Subjects :
- Pure mathematics
Class (set theory)
Applied Mathematics
General Mathematics
Stability (learning theory)
Function (mathematics)
Stability result
Measure (mathematics)
Metric (mathematics)
Convergence (routing)
Mathematics::Metric Geometry
Mathematics::Differential Geometry
Topology (chemistry)
Mathematics
Subjects
Details
- ISSN :
- 00217824
- Volume :
- 158
- Database :
- OpenAIRE
- Journal :
- Journal de Mathématiques Pures et Appliquées
- Accession number :
- edsair.doi...........53ad24dd7f3c30c81d27d72079af03fb