New Li--Yau--Hamilton Inequalities for the Ricci Flow via the Space-time Approach
Abstract
We generalize Hamilton's matrix Li-Yau-type Harnack estimate for the Ricci flow by considering the space of all LYH (Li-Yau-Hamilton) quadratics that arise as curvature tensors of space-time connections satisfying the Ricci flow with respect to the natural space-time degenerate metric. As a special case, we employ scaling arguments to derive a linear-type matrix LYH estimate. The new LYH quadratics obtained in this way are associated to the system of the Ricci flow coupled to a 1-form and a 2-form evolving by heat-type equations. In the case of a Kaehler solution, a special case of our linear-type trace LYH estimate is weaker than but qualitatively equivalent to Hamilton's trace estimate.
Keywords
Cite
@article{arxiv.math/9910022,
title = {New Li--Yau--Hamilton Inequalities for the Ricci Flow via the Space-time Approach},
author = {Bennett Chow and Dan Knopf},
journal= {arXiv preprint arXiv:math/9910022},
year = {2007}
}
Comments
This revision mostly makes changes in terminology to match the published version of the paper. In particular, we now call our estimates `Li--Yau--Hamilton inequalities'. (51 pages)