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http://dx.doi.org/10.4134/JKMS.2015.52.5.1097

SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD  

HAN, YINGBO (College of Mathematics and Information Science Xinyang Normal University)
ZHANG, WEI (School of Mathematics South China University of Technology)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.5, 2015 , pp. 1097-1108 More about this Journal
Abstract
In this paper, we investigate p-biharmonic maps u : (M, g) $\rightarrow$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if ${\int}_M|{\tau}(u)|^{{\alpha}+p}dv_g$ < ${\infty}$ and ${\int}_M|d(u)|^2dv_g$ < ${\infty}$, then u is harmonic, where ${\alpha}{\geq}0$ is a nonnegative constant and $p{\geq}2$. We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen's conjecture for p-biharmonic submanifolds).
Keywords
p-biharmonic maps; p-biharmoinc submanifolds;
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