Harnack estimates for a heat-type equation under the Ricci flow

DOI10.1016/j.jde.2015.10.024zbMath1330.53086OpenAlexW2174363494MaRDI QIDQ898557

Xiaorui Zhu, Yi Li

Publication date: 18 December 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.10.024

zbMATH Keywords

nonlinear parabolic equationRicci flowHarnack estimate

Mathematics Subject Classification ID

Related Items (17)

Gradient estimates for the weighted Lichnerowicz equation on smooth metric measure spaces ⋮ Parabolic gradient estimates and Harnack inequalities for a nonlinear equation under the Ricci flow ⋮ Gradient estimates of a nonlinear Lichnerowicz equation under the Finsler-geometric flow ⋮ Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space ⋮ Some general gradient estimates for two nonlinear parabolic equations along Ricci flow ⋮ Upper bounds of Hessian matrix and gradient estimates of positive solutions to the nonlinear parabolic equation along Ricci flow ⋮ Elliptic gradient estimates for a nonlinear heat equation and applications ⋮ Harnack inequality, heat kernel bounds and eigenvalue estimates under integral Ricci curvature bounds ⋮ Liouville theorems for nonlinear elliptic equations on Riemannian manifolds ⋮ Gradient estimates for the 𝑝-Laplacian Lichnerowicz equation on smooth metric measure spaces ⋮ Gradient estimates and Harnack inequalities of a parabolic equation under geometric flow ⋮ Gradient estimates and Harnack inequalities for a Yamabe-type parabolic equation under the Yamabe flow ⋮ Gradient estimates and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces ⋮ Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds ⋮ Li-Yau Harnack estimates for a heat-type equation under the geometric flow ⋮ Local parabolic and elliptic gradient estimates for a generalized heat-type equation under the Yamabe flow ⋮ Local elliptic gradient estimates for a nonlinear parabolic equation under the Ricci flow

Cites Work

• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds
• Gradient estimates for the heat equation under the Ricci flow
• On the parabolic kernel of the Schrödinger operator
• Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds
• Li-Yau estimates for a nonlinear parabolic equation on manifolds
• Gradient estimates for a nonlinear parabolic equation on complete non-compact Riemannian manifolds
• Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds

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