The Abresch-Gromoll inequality in a non-smooth setting (Q379826)

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.