Let $M^{n}$ be a complete oriented non-compact minimally immersed submanifold in a complete Riemannian manifold $N^{n+p}$ of non-negative curvature. We prove that if $M$ is super-stable, then there are no non-trivial $L^2$ harmonic one forms on $M$. This is a generalization of the main result in [8].
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机译：令$ M ^ {n} $是完全非负曲率的黎曼流形$ N ^ {n + p} $的完全定向非紧致最小浸入子流形。我们证明如果$ M $是超稳定的，则在$ M $上不存在非平凡的$ L ^ 2 $调和形式。这是[8]中主要结果的概括。
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