Liouville theorems of stable $F$-harmonic maps for compact convex hypersurfaces

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概要

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• Let $M^n$ be a compact convex hypersurface in $\mathbb{R}^{n+1}$. In this paper, we proved firstly that if the principal curvatures $\lambda_i$ of $M^n$ satisfy $0<\lambda_1\le\cdots\le\lambda_n$ and $\lambda_n<\sum_{j=1}^{n-1}\lambda_j$,then there exist no nonconstant stable $F$-harmonic map between $M$ and a compact Riemannian manifold when (1.2) or (1.3) holds (Theorem 1). This is the generalization or union of the corresponding results for several varieties of harmonic map. Then, when the target manifold is $\delta$-pinched, using a new estimate method, we obtain the Liouville-type theorem (Theorem 2) for stable $F$-harmonic map, which improve the results of M.Ara in [2].

• 広島大学の論文

著者

• Liu Jiancheng

  Department Of Mathematics Northwest Normal University Lanzhou 730070 China

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• Liouville theorems of stable $F$-harmonic maps for compact convex hypersurfaces

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