Liouville type theorem for $p$-harmonic maps II
Commun. Korean Math. Soc. 2014 Vol. 29, No. 1, 155-161
https://doi.org/10.4134/CKMS.2014.29.1.155
Printed January 31, 2014
Seoung Dal Jung
Jeju National University
Abstract : Let $M$ be a complete Riemannian manifold and let $N$ be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M \geq-{4(p-1)\over p^2}\mu_0$ at all $x\in M$ and ${\rm Vol}(M)$ is infinite, where $\mu_0>0$ is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on $M$. Then any $p$-harmonic map $\phi:M\to N$ of finite $p$-energy is constant. Also, we study Liouville type theorem for $p$-harmonic morphism.
Keywords : $p$-harmonic map, $p$-harmonic morphism, Liouville type theorem
MSC numbers : 53C43, 58E20
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