Liouville type theorems for p-harmonic maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:342

Article

Moon, Dong Joo¹  Liu, Huili²  Dal Jung, Seoung¹ 

[1] Jeju Natl Univ, Dept Math, Cheju 690756, South Korea

[2] Northeastern Univ, Dept Math, Shenyang 110004, Peoples R China

关键词: p-harmonic map;    p-harmonic morphism;    Liouville type theorem;   

DOI  :  10.1016/j.jmaa.2007.12.018

来源: Elsevier

【 摘 要 】

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that Ric(M) >= - 4(p-1)/p(2)mu(0) at all x is an element of M and > - 4(p-1)/p(2)mu(0) at some point x(0) is an element of M, where where mu(0) > 0 is the least eigenvalue of the Laplacian acting on L-2-functions on M. Let 2 <= q <= p. Then any q-harmonic map phi: M -> N of finite q-energy is constant. Moreover, if N is a Riemannian manifold of non-positive scalar curvature, then any q-harmonic morphism phi: M -> N of finite q-energy is constant. (C) 2007 Elsevier Inc. All rights reserved.

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