English

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

R2 v1 2026-06-24T08:50:15.170Z