An upper bound of the heat kernel along the harmonic-Ricci flow

Abstract

In this paper, we first derive a Sobolev inequality along the harmonic-Ricci flow. We then prove a linear parabolic estimate based on the Sobolev inequality and Moser's iteration. As an application, we will obtain an upper bound estimate for the heat kernel under the flow.

16pages. arXiv admin note: text overlap with arXiv:1412.3200 by other authors

References in corpus (1)

• The logarithmic Sobolev inequality along the Ricci flow