The Abresch-Gromoll inequality in a non-smooth setting
Nicola Gigli, Sunra Mosconi
TL;DR
This paper extends the Abresch-Gromoll inequality to non-smooth metric measure spaces with Ricci curvature bounds, showing it holds in the same form as on smooth Riemannian manifolds.
Contribution
It proves the Abresch-Gromoll inequality in the setting of infinitesimally Hilbertian CD(K,N) spaces, generalizing the classical result to non-smooth spaces.
Findings
The inequality holds in non-smooth CD(K,N) spaces.
The form of the inequality matches the smooth case.
The result bridges smooth and non-smooth geometric analysis.
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometric and Algebraic Topology