Parabolic frequency on Ricci flows
Differential Geometry
2022-08-01 v2 Analysis of PDEs
Abstract
This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple proof of backwards uniqueness. For solutions of more general parabolic equations on a Ricci flow, this paper provides bounds on the derivative of the frequency, which similarly imply backwards uniqueness.
Keywords
Cite
@article{arxiv.2201.05505,
title = {Parabolic frequency on Ricci flows},
author = {Julius Baldauf and Dain Kim},
journal= {arXiv preprint arXiv:2201.05505},
year = {2022}
}
Comments
14 pages; final version published in IMRN