English

Estimating the trace-free Ricci tensor in Ricci flow

Differential Geometry 2007-11-08 v1 Analysis of PDEs

Abstract

An important and natural question in the analysis of Ricci flow singularity formation in dimensions four and above is as follows: What are the weakest conditions that provide control of the norm of the Riemann curvature tensor? In this short note, we show that on a compact manifold, the trace-free Ricci tensor is controlled in a precise fashion by the other components of the irreducible decomposition of the curvature tensor, without any hypotheses on the initial data.

Keywords

Cite

@article{arxiv.0711.1153,
  title  = {Estimating the trace-free Ricci tensor in Ricci flow},
  author = {Dan Knopf},
  journal= {arXiv preprint arXiv:0711.1153},
  year   = {2007}
}
R2 v1 2026-06-21T09:41:04.107Z