Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774529 | Journal of Mathematical Analysis and Applications | 2017 | 21 Pages |
Abstract
Suppose G is a compact Lie group, H is a closed subgroup of G, and the homogeneous space G/H is connected. The paper investigates the Ricci flow on a manifold M diffeomorphic to [0,1]ÃG/H. First, we prove a short-time existence and uniqueness theorem for a G-invariant solution g(t) satisfying the boundary condition II(g(t))=F(t,gâM(t)) and the initial condition g(0)=gË. Here, II(g(t)) is the second fundamental form of âM, gâM is the metric induced on âM by g(t), F is a smooth map and gË is a metric on M. Second, we study Perelman's F-functional on M. Our results show, roughly speaking, that F is non-decreasing on a G-invariant solution to the modified Ricci flow, provided that this solution satisfies boundary conditions inspired by a paper of Gianniotis.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Artem Pulemotov,