Differential Harnack estimates for conjugate heat equation under the\n Ricci flow

2014/09/03 by Abimbola Abolarinwa, Abolarinwa, Abimbola
Mathematics · #35K08 #53C44 #58J35 #58J60 #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1409.1038

openalex publication_date 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove certain localized and global differential Harnack inequality for all\npositive solutions to the geometric conjugate heat equation coupled to the\nforward in time Ricci flow. In this case, the diffusion operator is perturbed\nwith the curvature operator, precisely, the Laplace-Beltrami operator is\nreplaced with " \Δ - R(x,t)", where R is the scalar curvature of the\nRicci flow, which is well generalised to the case of nonlinear heat equation\nwith potential. Our estimates improve on some well known results by weakening\nthe curvature constraints. As a by product, we obtain some Li-Yau type\ndifferential Harnack estimate. The localized version of our estimate is very\nuseful in extending the results obtained to noncampact case.\n

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