The Abresch-Gromoll inequality in a non-smooth setting
type: Item
instance of: scholarly article
title: The Abresch-Gromoll inequality in a non-smooth setting
zbMATH Open document ID: 1280.53038
author: Nicola Gigli
author: Sunra J. N. Mosconi
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-11-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.3813
reviewed by: Jean-Pierre Magnot
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 28C15
Mathematics Subject Classification ID: 53C70
Mathematics Subject Classification ID: 46E27
zbMATH DE Number: 6224695
zbMATH Keywords: metric geometry
zbMATH Keywords: lower Ricci bound
zbMATH Keywords: mm-spaces
MaRDI profile type: Publication
OpenAlex ID: W2950782143
arXiv ID: 1209.3813
cites work: On Complete Manifolds With Nonnegative Ricci Curvature
cites work: Q3055493
cites work: Nonlinear potential theory on metric spaces
cites work: Differentiability of Lipschitz functions on metric measure spaces
cites work: Lower bounds on Ricci curvature and the almost rigidity of warped products
cites work: On the heat flow on metric measure spaces: existence, uniqueness and stability
cites work: Heat Flow on Alexandrov Spaces
cites work: A PDE approach to nonlinear potential theory in metric measure spaces
cites work: Weak curvature conditions and functional inequalities
cites work: Ricci curvature for metric-measure spaces via optimal transport
cites work: Local Poincaré inequalities from stable curvature conditions on metric spaces
cites work: Q4257729
cites work: On the geometry of metric measure spaces. I
cites work: On the geometry of metric measure spaces. II
cites work: Optimal Transport
cites work: On a new definition of Ricci curvature on Alexandrov spaces
DOI: 10.3934/DCDS.2014.34.1481
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review text: The author gets an inequality for metric measure spaces in the class of infinitesimally Hilbertian spaces, which are mm-spaces with Ricci curvature bounded from below and dimension bounded from above. This work is a non-trivial extension of a result of \textit{U. Abresch} and \textit{D. Gromoll} [J. Am. Math. Soc. 3, No. 2, 355--374 (1990; Zbl 0704.53032)]. The authors develop a method based on a deep analysis of Abresch and Gromoll's proof, and check step by step that the key arguments that they identified are also true in the framework considered. NEWLINENEWLINENEWLINEThe methods employed makes this papers very interesting for beginners in mm-spaces, because of the exposition of standard tools.
description: scientific article; zbMATH DE number 6224695