An almost rigidity Theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth
Differential Geometry
2017-10-17 v1
Abstract
The main results of this paper consists of two parts. Firstly, we obtain an almost rigidity theorem which says that on a RCD(0, N) space, when a domain between two level sets of a distance function has almost maximal volume compared to that of a cylinder, then this portion is close to a cylinder as a metric space. Secondly, we apply this almost rigidity theorem to study noncompact RCD(0, N) spaces with linear volume growth. More precisely, we obtain the sublinear growth of diameter of geodesic spheres, and study the non-existence of harmonic functions with polynomial growth on such RCD(0,N) spaces.
Keywords
Cite
@article{arxiv.1710.05830,
title = {An almost rigidity Theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth},
author = {Xian-Tao Huang},
journal= {arXiv preprint arXiv:1710.05830},
year = {2017}
}
Comments
40 pages