The linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation
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- by Bennett Chow and Peng Lu PDF
- Proc. Amer. Math. Soc. 141 (2013), 2855-2857 Request permission
Abstract:
We show that on steady and shrinking gradient Ricci solitons, expressions involving the linear trace Harnack quadratic satisfy the heat equation. We also interpolate between Li–Yau-type calculations of Cao–Hamilton and Perelman.References
- Xiaodong Cao and Richard S. Hamilton, Differential Harnack estimates for time-dependent heat equations with potentials, Geom. Funct. Anal. 19 (2009), no. 4, 989–1000. MR 2570311, DOI 10.1007/s00039-009-0024-4
- Bennett Chow and Richard S. Hamilton, Constrained and linear Harnack inequalities for parabolic equations, Invent. Math. 129 (1997), no. 2, 213–238. MR 1465325, DOI 10.1007/s002220050162
- Richard S. Hamilton, The Harnack estimate for the Ricci flow, J. Differential Geom. 37 (1993), no. 1, 225–243. MR 1198607
- Lei Ni, A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature, J. Amer. Math. Soc. 17 (2004), no. 4, 909–946. MR 2083471, DOI 10.1090/S0894-0347-04-00465-5
- Lei Ni, A matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow, J. Differential Geom. 75 (2007), no. 2, 303–358. MR 2286824
- Grisha Perelman, The entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159.
Additional Information
- Bennett Chow
- Affiliation: Department of Mathematics, University of California San Diego, La Jolla, California 92093
- MR Author ID: 229249
- Peng Lu
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
- MR Author ID: 308539
- Received by editor(s): September 13, 2011
- Published electronically: April 19, 2013
- Communicated by: Michael Wolf
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2855-2857
- MSC (2010): Primary 53C44
- DOI: https://doi.org/10.1090/S0002-9939-2013-12176-3
- MathSciNet review: 3056575