Gradient estimates for the heat equation under the Ricci-harmonic map flow
Gradient estimates for the heat equation under the Ricci-harmonic map flow
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 $M$ …