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Li–Yau-Type Gradient Estimate along Geometric Flow

Author

Listed:
  • Shyamal Kumar Hui

    (Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, India)

  • Abimbola Abolarinwa

    (Department of Mathematics, University of Lagos, Akoka 101017, Lagos State, Nigeria)

  • Meraj Ali Khan

    (Department of Mathematics and Statistics, Imam Muhammad Ibn Saud Islamic University, Riyadh 11566, Saudi Arabia)

  • Fatemah Mofarreh

    (Department of Mathematical Science, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia)

  • Apurba Saha

    (Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, India)

  • Sujit Bhattacharyya

    (Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, India)

Abstract

In this article we derive a Li–Yau-type gradient estimate for a generalized weighted parabolic heat equation with potential on a weighted Riemannian manifold evolving by a geometric flow. As an application, a Harnack-type inequality is also derived in the end.

Suggested Citation

  • Shyamal Kumar Hui & Abimbola Abolarinwa & Meraj Ali Khan & Fatemah Mofarreh & Apurba Saha & Sujit Bhattacharyya, 2023. "Li–Yau-Type Gradient Estimate along Geometric Flow," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1364-:d:1094225
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    References listed on IDEAS

    as
    1. Yanlin Li & Abimbola Abolarinwa & Ali H. Alkhaldi & Akram Ali, 2022. "Some Inequalities of Hardy Type Related to Witten–Laplace Operator on Smooth Metric Measure Spaces," Mathematics, MDPI, vol. 10(23), pages 1-13, December.
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