An interpolating harnack inequality for nonlinear heat equation on a surface

Abstract

In this short note we prove new differential Harnack inequalities interpolating those for the static surface and for the Ricci flow. In particular, for 0 ≤ ε ≤ 1, α ≥ 0, β ≥ 0, γ ≤ 1 and u being a positive solution to (formula presented) on closed surfaces under the flow(formula presented) with R > 0, we prove that (formula presented).