Abstract
We obtain the Harnack estimate of the solution to H k-flow in Euclidean space ℝn+1, for k > 0. By using this estimate, we get some corollaries about the translation soliton.
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References
Li P, Yau S T. On the parabolic kernel of the Schrödinger operator. Acta Math, 156: 153–201 (1986)
Hamilton R. A matrix Harnack estimate for the heat equation. Comm Anal Geom, 1: 113–126 (1993)
Hamilton R. The Ricci flow on surfaces, In: Contemp Math, vol 71. Providence: Amer Math Soc, 1998, 237–262
Hamilton R. The Harnack estimate for the mean curvature flow. J Diff Geom, 41: 215–226 (1995)
Hamilton R. The Harnack estimate for the ricci flow. J Differ Geom, 37: 225–243 (1993)
Chow B. On Harnack’s inequality and entropy for the Gaussian curvature flow. Comm Pure Appl Math, 44: 469–483 (1991)
Chow B. The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature. Comm Pure Appl Math, 45: 1003–1014 (1992)
Schulze F. Evolution of convex hypersurfaces by powers of the mean curvature. Math Z, 251: 721–733 (2005)
Andrews Ben. Harnack inequalities for evolving hypersurfaces. Math Z, 215: 179–197 (1994)
Schoen R, Yan S T. Lectures on Differetial Geometry. Someruille: International Press, 1995
Sheng W M. Geometry of complete hypersurfaces evolved by mean curvature flow. Chin Ann Math, 24: 123–132(2003)
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Wang, J. Harnack estimate for the H k-flow. SCI CHINA SER A 50, 1642–1650 (2007). https://doi.org/10.1007/s11425-007-0095-3
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DOI: https://doi.org/10.1007/s11425-007-0095-3