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The first eigenvalue of spacelike submanifolds in indefinite space form

Yingbo Han, Shuxiang Feng (2011)

Archivum Mathematicum

In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.

The gaps in the spectrum of the Schrödinger operator

Haizhong Li, Linlin Su (2005)

Banach Center Publications

We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.

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