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

Title & Authors
SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD
HAN, YINGBO; ZHANG, WEI;

Abstract
In this paper, we investigate p-biharmonic maps u : (M, g) $\small{\rightarrow}$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if $\small{{\int}_M|{\tau}(u)|^{{\alpha}+p}dv_g}$ < $\small{{\infty}}$ and $\small{{\int}_M|d(u)|^2dv_g}$ < $\small{{\infty}}$, then u is harmonic, where $\small{{\alpha}{\geq}0}$ is a nonnegative constant and $\small{p{\geq}2}$. We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with $\small{c{\leq}0}$ 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;
Language
English
Cited by
1.
SOME RESULTS OF EXPONENTIALLY BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD, Bulletin of the Korean Mathematical Society, 2016, 53, 6, 1651
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