Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2015.01.15
  • Published : 2015.09.01
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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).

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