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arXiv · 2105.14386

Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds

Bing Wang·Hui-Chun Zhang
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Abstract

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.

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Bing Wang, Hui-Chun Zhang. 2021-05-29. Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds. https://arxiv.org/abs/2105.14386

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