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The gaps in the spectrum of the Schrödinger operator

Haizhong LiLinlin 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 R N 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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