An almost rigidity theorem and its applications to noncompact RCD(0, N) spaces with linear volume growth

作者：Huang, Xian-Tao^*

来源：Communications in Contemporary Mathematics, 2020, 22(4): 1850076.

DOI：10.1142/S0219199718500761

• RCD(0, N) space
• almost rigidity theorem
• distance function
• Busemann function
• harmonic function

The main results of this paper consist of two parts. First, we obtain an almost rigidity theorem which roughly says that on an 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. Second, 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 problem of nonconstant harmonic functions with polynomial growth on such RCD(0, N) spaces.

• 出版日期2020-6
• 单位中山大学