Resumen de Remarks on Liouville-type theorems on complete noncompact Finsler manifolds
Songting Yin, Pan Zhang
We give a gradient estimate of the positive solution to the equation ∆u = −λ 2u, λ ≥ 0 on a complete noncompact Finsler manifold. Then we obtain the corresponding Liouville-type theorem and Harnack inequality for the solution. Moreover, on a complete noncompact Finsler manifold we also prove a Liouville-type theorem for a C2 -nonnegative function f satisfying ∆f ≥ cfd, c > 0, d > 1, which improves a result obtained by Yin and He.
