## 摘要

We introduce and study an approximate solution of the p-Laplace equation and a linearlization ℒ_{ϵ} of a perturbed p-Laplace operator. By deriving an ℒ_{ϵ}-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 |
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頁（從 - 到） | 787-825 |

頁數 | 39 |

期刊 | Transactions of the American Mathematical Society |

卷 | 368 |

發行號 | 2 |

DOIs | |

出版狀態 | 已發佈 - 2016 2月 |

## ASJC Scopus subject areas

- 數學(全部)
- 應用數學