# Liouville properties for p-harmonic maps with finite q-energy

Shu Cheng Chang, Jui Tang Chen, Shihshu Walter Wei

16 引文 斯高帕斯（Scopus）

## 摘要

We introduce and study an approximate solution of the p-Laplace equation and a linearlization ℒϵ of a perturbed p-Laplace operator. By deriving an ℒϵ-type Bochner’s formula and Kato type inequalities, we prove a Liouville type theorem for weakly p-harmonic functions with finite p-energy on a complete noncompact manifold M which supports a weighted Poincaré inequality and satisfies a curvature assumption. This nonexistence result, when combined with an existence theorem, yields in turn some information on topology, i.e. such an M has at most one p-hyperbolic end. Moreover, we prove a Liouville type theorem for strongly p-harmonic functions with finite q-energy on Riemannian manifolds. As an application, we extend this theorem to some p-harmonic maps such as p-harmonic morphisms and conformal maps between Riemannian manifolds. In particular, we obtain a Picard-type theorem for p-harmonic morphisms.

原文 英語 787-825 39 Transactions of the American Mathematical Society 368 2 https://doi.org/10.1090/tran/6351 已發佈 - 2016 二月

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