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Hamilton’s Harnack inequality and the W-entropy formula on complete Riemannian manifolds

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  • Li, Xiang-Dong

Abstract

In this paper, we prove Hamilton’s Harnack inequality and the gradient estimates of the logarithmic heat kernel for the Witten Laplacian on complete Riemannian manifolds. As applications, we prove the W-entropy formula for the Witten Laplacian on complete Riemannian manifolds, and prove a family of logarithmic Sobolev inequalities on complete Riemannian manifolds with natural geometric condition.

Suggested Citation

  • Li, Xiang-Dong, 2016. "Hamilton’s Harnack inequality and the W-entropy formula on complete Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1264-1283.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:4:p:1264-1283
    DOI: 10.1016/j.spa.2015.11.002
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    References listed on IDEAS

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    1. Arnaudon, Marc & Thalmaier, Anton & Wang, Feng-Yu, 2009. "Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3653-3670, October.
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    Cited by:

    1. Kuwae, Kazuhiro & Li, Songzi & Li, Xiang-Dong & Sakurai, Yohei, 2024. "Liouville theorem for V-harmonic maps under non-negative (m,V)-Ricci curvature for non-positive m," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    2. Abolarinwa, Abimbola & Taheri, Ali, 2021. "Elliptic gradient estimates for a nonlinear f-heat equation on weighted manifolds with evolving metrics and potentials," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Li, Xue-Mei & Thompson, James, 2018. "First order Feynman–Kac formula," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3006-3029.

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