Gradient estimates for a weighted parabolic equation under geometric flow

Abstract

Let (M n , g, e −φ dv) be a weighted Riemannian manifold evolving by geometric flow ∂g ∂t = 2h(t), ∂φ ∂t = ∆φ. In this paper, we obtain a series of space-time gradient estimates for positive solutions of a parabolic partial equationon a weighted Riemannian manifold under geometric flow. By integrating the gradient estimates, we find the corresponding Harnack inequalities.

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

“…[2][3][4][5]. The studies on gradient estimates and differential Harnack inequalities were presented in [6][7][8][9][10][11]. We can find some papers regarding different manifolds of different connections in a tangent bundle [12][13][14][15][16][17][18].…”

Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications

“…Along different geometric flows, he also obtained Li-Yau-type estimates and Perelman-type differential Harnack inequalities. Differential Harnack estimates and gradient estimates were studied in [6,[17][18][19][20][21][22][23][24][25]. In recent studies, a group of researchers have made advancements in the field of special submanifolds within various spaces [26][27][28][29][30][31][32][33][34][35][36][37][38].…”