Non-branching RCD(0, N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

作者：Kitabeppu Yu^*; Lakzian Sajjad

来源：Canadian Mathematical Bulletin, 2015, 58(4): 787-798.

DOI：10.4153/CMB-2015-052-4

• Milnor conjecture
• non negative Ricci curvature
• curvature dimension condition
• finitely generated
• fundamental group
• infinitesimally Hilbertian

In this paper, we generalize the finite generation result of Sormani to non-branching RCD (0, N) geodesic spaces (and in particular, Alexandroy spaces) with full support measures. This is a special case of the Minor's Conjecture for complete non-compact RCD (0, N) spaces. One of the key tools we use is the Abresch-Gromoll type excess estimates for non-smooth spaces obtained by Gigli-Mosconi.

• 出版日期2015-12