Li–Yau-Type Gradient Estimate along Geometric Flow

Shyamal Kumar Hui, Abimbola Abolarinwa, Meraj Ali Khan (), Fatemah Mofarreh, Apurba Saha and Sujit Bhattacharyya
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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

Mathematics, 2023, vol. 11, issue 6, 1-15

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.

Keywords: gradient estimate; weighted Laplacian; parabolic equation; geometric flow (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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