We consider a compact, orientable minimal hypersurfaces of the unit sphere and prove a comparison theorem between the spectrum of the stability operator and that of the Laplacian on 1-forms. As a corollary, we show that the index is bounded below by a linear function of the first Betti number; in particular, if the first Betti number is large, then the immersion is highly unstable.
Index bounds for minimal hypersurfaces of the sphere / Savo, Alessandro. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 59:3(2010), pp. 823-837. [10.1512/iumj.2010.59.4013]
Index bounds for minimal hypersurfaces of the sphere
SAVO, Alessandro
2010
Abstract
We consider a compact, orientable minimal hypersurfaces of the unit sphere and prove a comparison theorem between the spectrum of the stability operator and that of the Laplacian on 1-forms. As a corollary, we show that the index is bounded below by a linear function of the first Betti number; in particular, if the first Betti number is large, then the immersion is highly unstable.File allegati a questo prodotto
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