Remarks on Liouville-type theorems on complete noncompact Finsler manifolds

Songting Yin ^[1] ; Pan Zhang ^[2]
1. [1] Tongling University
  
  Tongling University
  
  China
2. [2] University of Science and Technology of China
  
  University of Science and Technology of China
  
  China
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 59, Nº. 2, 2018, págs. 255-264
Idioma: inglés
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Resumen
- 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.