On an alternate proof of Hamilton's matrix Harnack inequality for the Ricci flow

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dc.creatorChow, Bennett
dc.date2001-10-24
dc.date.accessioned2026-07-07T04:44:02Z
dc.date.available2026-07-07T04:44:02Z
dc.descriptionBased 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 2-forms Whitney sum 1-forms is nonnegative. The idea is to consider the 2-form which minimizes the associated quadratic form to obtain a symmetric 2-tensor. A long but straightforward computation implies this 2-tensor is a subsolution to heat-type equation. A standard application of the maximum principle implies the result.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0110261
dc.identifierhttp://arxiv.org/abs/math/0110261
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62477
dc.subjectDifferential Geometry
dc.subject53C44; 58J35; 35K55; 35K57
dc.titleOn an alternate proof of Hamilton's matrix Harnack inequality for the Ricci flow
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