Gradient estimates for the heat equation under the Ricci-Harmonic Map flow

Abstract

The paper establishes a series of gradient estimates for positive solutions to the heat equation on a manifold $M$ evolving under the Ricci flow, coupled with the harmonic map flow between $M$ and a second manifold $N$. We prove Li-Yau type Harnack inequalities and we consider the cases when $M$ is a complete manifold without boundary and when $M$ is compact, without boundary.

13 pages

References in corpus (2)

• Gradient estimates for the heat equation under the Ricci flow
• Stability of solutions of certain extended Ricci flow systems

Cited by in corpus (4)

• Smooth long-time existence of Harmonic Ricci Flow on surfaces
• Gradient estimates for a nonlinear parabolic equation with potential under geometric flow
• Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures
• Gradient estimates and parabolic frequency under the Laplacian G_2 flow