A generalization of Hamilton's differential Harnack inequality for the Ricci flow

By S. Brendle. 2007

56 citations recorded by the source corpus.

In [10], R. Hamilton established a differential Harnack inequality for solutions to the Ricci flow with nonnegative curvature operator. We show that this inequality holds under the weaker condition that M x R^2 has nonnegative isotropic curvature.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0d94b77adceb5fc0788b50a75b538a167b04fb90

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities (2010, unknown): “The theorem recovers Brendle’s recent generalization of Hamilton’s Harnack inequality by putting S = {(A, v) | A ∈ so(n,C), rank(A) = 2, v ∈ A(Cn)} As is shown in [Brendle, 2009] this still implies the usual trace Harnack inequality.”
Expanding solitons with non-negative curvature operator coming out of cones (2010, background): “Brendle [1] at this point to show that (X, g̃(t)) is an expanding gradient soliton.”
Ricci flow with surgery on manifolds with positive isotropic curvature (2017, background): “In [3], we showed that the differential Harnack inequality holds on any solution to the Ricci flow which is weakly PIC2.”
How to produce a Ricci Flow via Cheeger-Gromoll exhaustion (2011, methodology): “But under our weaker assumption we can replace them by Brendle’s [5] trace Harnack inequality and the strong maximum principle of Brendle and Schoen [7, Proposition 9] (see also [50, Appendix]).”