p-harmonic functions on complete manifolds with a weighted Poincaré inequality

Bui Van Binh; Nguyen Thac Dung; Nguyen Thi Le Hai

doi:10.2996/kmj/1499846601

Bui Van Binh, Nguyen Thac Dung, Nguyen Thi Le Hai

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Keywords: p-harmonic function, p-Laplacian, the first eigenvalue, connectedness at infinity, minimal hypersurfaces

JOURNAL FREE ACCESS

2017 Volume 40 Issue 2 Pages 343-357

DOI https://doi.org/10.2996/kmj/1499846601

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Abstract

In this paper, we consider p-harmonic functions on complete Riemannian manifolds and give different proofs of some main theorems by Chang-Chen-Wei, in [3]. Moreover, we are able to refine their results in case of weakly p-harmonic functions. Some applications to study the connectedness at infinity of stable minimal hypersurfaces are also given.

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