Analysis Seminar

Kazuhiro KuwaeFukuoka University
RCD*(K,N)-spaces is a metric measure space generalizing Riemmanian manifolds with lower Ricci bound K(in R) and an upper bound N being greater than 1 and finite.This class of spaces also contains the class of N-dimenasional Alexandrov spaces, which was proved by Petrunin, Zhang-Zhu,and also contains the class of weighted Riemannian manifolds with Witten Laplacian and lower bound K of $N$-Bakry-Emery Ricci tensor. I will talk on the stochastic expression of radial process under the law for all starting point including the reference point appeared in the radial function provided the reference point fulfills a regularity condition depending on the geometric structure of the RCD*(K,N)-space. The expression of radial process is completely different from Kendall’s expression (1987) including the local time on cut-locus without lower Ricci bound in the framework of Riemannian manifold. Our expression of radial process does not contain the local time on cut-locus. Instead of it, we extract a positive additive continuous functional, which can thought of continuous additive functionals corresponding to the difference of Laplacians of radial functions between on the given space and on the model space.