A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows
Analysis of PDEs
2016-09-29 v2 Differential Geometry
Abstract
It is the purpose of this article to establish a technical tool to study regularity of solutions to parabolic equations on manifolds. As applications of this technique, we prove that solutions to the Ricci-DeTurck flow, the surface diffusion flow and the mean curvature flow enjoy joint analyticity in time and space, and solutions to the Ricci flow admit temporal analyticity.
Keywords
Cite
@article{arxiv.1309.2043,
title = {A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows},
author = {Yuanzhen Shao},
journal= {arXiv preprint arXiv:1309.2043},
year = {2016}
}