Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds

摘要

In this paper, we generalize Liouville type theorems for some semilinear partial differential inequalities to sub-Riemannian manifolds satisfying a nonnegative generalized curvature -dimension inequality introduced by Baudoin and Garofalo in [5]. In particular, our results apply to all Sasakian manifolds with nonnegative horizontal Webster-Tanaka-Ricci curvature. The key ingredient is to construct a class of "good" cut-off functions. We also provide some upper bounds for lifespan to parabolic and hyperbolic inequalities. (c) 2023 Elsevier Inc. All rights reserved.