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Harnack Estimate for Positive Solutions to a Nonlinear Equation Under Geometric Flow
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In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds. We shall get an interesting Harnack inequality as an application.
Abstract
In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds. We shall get an interesting Harnack inequality as an application.
참고문헌 (10)
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- B. Chow, "The Ricci flow; An introduction" (2004), AMS
- R. S. Hamilton, "The Harnack estimate for the Ricci flow", J. Differ. Geom, 37(1), pp.225~243 (1993)
- S. Kuang, "A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow", J. Funct. Anal, 255(4), pp.1008~1023 (2008)
- P. Li, "On the parabolic kernel of the Schr¨odinger operator", Acta Math, 156(3-4), pp.153~201 (1986)
- S. P. Liu, "Gradient estimates for solutions of the heat equation under Ricci flow", Pacific J. Math, 243(1), pp.165~180 (2009)
- G. Perelman, "The entropy formula for the Ricci flow and its geometric applications", arXiv: math, 2002
- J. Sun, "Gradient estimates for positive solutions of the heat equation under geometric flow", Pacific J. Math, 253(2), pp.489~510 (2011)
- J. Y. Wu, "Gradient estimates for a nonlinear parabolic equation and Liouville theorems", Manuscripta mathematica, 159(3-4), pp.511~547 (2019)
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