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.
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}
}