A geometric interpretation of Hamilton's Harnack inequality for the Ricci flow

By Bennett Chow, Sun-Chin Chu. 2002

67 citations recorded by the source corpus.

We give a geometric interpretation of Hamilton's matrix Harnack inequality for the Ricci flow as the curvature of a connection on space-time.

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

View Paper: https://www.semanticscholar.org/paper/7979725e8ed8fe9b6206db09416238c61c08a64a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Huaihuo Cao
2. S. Brendle
3. Reto Müller
4. Xiping Zhu
5. Lei Ni
6. Xiaohua Zhu
7. B.-l. Chen
8. Brett Kotschwar

In Astronomy and Astrophysics

1. Huaihuo Cao
2. Reto Müller
3. S. Brendle
4. Lei Ni
5. Xiping Zhu
6. Xiaohua Zhu
7. B.-l. Chen
8. Binglong Chen

In Geometry and Topology

1. Huaihuo Cao
2. Reto Müller
3. S. Brendle
4. Xiping Zhu
5. Lei Ni
6. Xiaohua Zhu
7. B.-l. Chen
8. Brett Kotschwar

Citations in the corpus

• A generalization of Hamilton's differential Harnack inequality for the Ricci flow (2007, background): “109, 247–263 (1992) [5] B. Chow and S.C. Chu, A geometric interpretation of Hamilton’s Harnack inequality for the Ricci flow, Math.”
• Recent developments on the Hamilton’s Ricci Flow (2007, background): “The intuition of forming a Type II singularity on compact manifolds was described by Hamilton [47] (see also [28] and [99]) and the existence of a Type II singularity on compact manifolds was also proposed as an open question in the introduction of the book of Chow-Lu-Ni [29].”
• A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow (2006, methodology): “Such an interpretation of the Li-Yau-Hamilton quadratic as a curvature operator on the space M × R was found by Chow and Chu [38] where a potentially degenerate Riemannian metric on M ×R+ was constructed.”
• Hamilton-Perelman's Proof of the Poincar\'e Conjecture and the Geometrization Conjecture (2006, background): “Such an interpretation of the Li-Yau-Hamilton quadratic as a curvature operator on the space M × R+ was found by Chow and Chu [39] where a potentially degenerate Riemannian metric on M × R+ was constructed.”
• Differential Harnack inequalities and the Ricci flow (2006, background): “The details can be found in their papers [5] and [6].”
• A matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow (2007, background): “See also [ CC1 -2], [CH], [CK1], [NT1], etc, for the later developments, [A] and references therein for the Li-Yau-Hamilton estimates of other geometric flows.”
• A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities (2010, unknown): “This is in fact a simple consequence of the work of Chow and Chu [1995], see also [Chow and Knopf, 2002].”