The Abresch-Gromoll inequality in a non-smooth setting

Nicola Gigli; Sunra Mosconi

doi:10.3934/dcds.2014.34.1481

Article Contents

2014, Volume 34, Issue 4: 1481-1509. Doi: 10.3934/dcds.2014.34.1481

This issue Previous Article Remarks on multi-marginal symmetric Monge-Kantorovich problems Next Article Hessian metrics, $CD(K,N)$-spaces, and optimal transportation of log-concave measures

The Abresch-Gromoll inequality in a non-smooth setting

Nicola Gigli^1, and
Sunra Mosconi^2,

1.
Université de Nice, Mathématiques, Parc Valrose, 06108 Nice
2.
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania

Received: August 31, 2012

Revised: October 31, 2012

Published: March 2014

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Abstract

We prove that the Abresch-Gromoll inequality holds on infinitesimally Hilbertian $CD(K,N)$ spaces in the same form as the one available on smooth Riemannian manifolds.

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Mathematics Subject Classification: Primary: 51Fxx; Secondary: 53C21.

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