$L^2$ harmonic 1-forms on minimal submanifolds in hyperbolic space

Details $L^2$ harmonic 1-forms on minimal submanifolds in hyperbolic space $L^2$ harmonic 1-forms on minimal submanifolds in hyperbolic space

2010-07-05

arxiv.org/abs/1007.0663v1

Mathematics

Differential Geometry

6 pages, to appear in Journal of Mathematical Analysis and Applications

Scientific paper

In this paper, we prove the nonexistence of $L^2$ harmonic 1-forms on a
complete super stable minimal submanifold $M$ in hyperbolic space under the
assumption that the first eigenvalue $\lambda_1 (M)$ for the Laplace operator
on $M$ is bounded below by $(2n-1)(n-1)$. Moreover, we provide sufficient
conditions for minimal submanifolds in hyperbolic space to be super stable.

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