On the Heat Kernel under the Ricci Flow Coupled with the Harmonic Map Flow

Abstract

We estimate the heat kernel on a closed Riemannian manifold $M$, with $dim(M)\ge 3$, evolving under the Ricci-harmonic map flow and the result depends on some constants arising from a Sobolev imbedding theorem. In a special case, when the scalar curvature satisfies a certain natural inequality, we obtain, as a corollary, a bound similar to the one known for the fixed metric case.

11 pages. arXiv admin note: substantial text overlap with arXiv:1010.5543

References in corpus (1)

• A Gaussian upper bound of the conjugate heat equation along an extended Ricci flow

Cited by in corpus (1)

• Smooth long-time existence of Harmonic Ricci Flow on surfaces