On an alternate proof of Hamilton's matrix Harnack inequality for the Ricci flow
Abstract
Based on a suggestion of Richard Hamilton, we give an alternate proof of his matrix Harnack inequality for solutions of the Ricci flow with positive curvature operator. This Harnack inequality says that a certain endomorphism, consisting of an expression in the curvature and its first two covariant derivatives, of the bundle of 2forms Whitney sum 1forms is nonnegative. The idea is to consider the 2form which minimizes the associated quadratic form to obtain a symmetric 2tensor. A long but straightforward computation implies this 2tensor is a subsolution to heattype equation. A standard application of the maximum principle implies the result.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110261
 Bibcode:
 2001math.....10261C
 Keywords:

 Mathematics  Differential Geometry;
 53C44;
 58J35;
 35K55;
 35K57
 EPrint:
 9 pages