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

Shu Cheng Chang, Jui Tang Chen, Shihshu Walter Wei

研究成果: 雜誌貢獻文章同行評審

12 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
頁(從 - 到)787-825
頁數39
期刊Transactions of the American Mathematical Society
368
發行號2
DOIs
出版狀態已發佈 - 2016 二月

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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