Gradient estimates of a nonlinear Lichnerowicz equation under the Finsler-geometric flow

Abstract

Let (Mn, F(t), m), t ∈ [0, T], be a compact Finsler manifold with F(t) evolving by the Finsler-geometric flow , where g(t) is the symmetric metric tensor associated with F, and h(t) is a symmetric (0, 2)-tensor. In this paper, we study gradient estimates for positive solutions of a nonlinear Lichnerowicz equation under Finsler-geometric flow , where c, p are two constants and p > 0. We obtain a global estimate and a Harnack estimate for positive solutions. Our results are also natural extension of similar results on Riemannian-geometric flow.