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The first eigenvalue of the Laplacian of an isoparametric minimal hypersurface in a unit sphere - MaRDI portal

The first eigenvalue of the Laplacian of an isoparametric minimal hypersurface in a unit sphere (Q1107140)

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scientific article; zbMATH DE number 4063987
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English
The first eigenvalue of the Laplacian of an isoparametric minimal hypersurface in a unit sphere
scientific article; zbMATH DE number 4063987

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    The first eigenvalue of the Laplacian of an isoparametric minimal hypersurface in a unit sphere (English)
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    1988
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    This is an interesting paper about the following open problem: Let x: \(M_{n-1}\to S^ n(1)\) be a closed minimal hypersurface in the unit n- sphere. The first eigenvalue \(\lambda_ 1\) of the Laplacian satisfies \(\lambda_ 1\leq n-1\) (Takahashi). For which manifolds is \(\lambda_ 1=n-1?\quad -\) The author gives partial answers for classes of isoparametric minimal hypersurfaces (and lower estimates also for higher eigenvalues \(\lambda_ k)\).
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    isoparametric hypersurfaces
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    minimal hypersurface
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    unit n-sphere
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    first eigenvalue
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    Laplacian
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