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Pré-Publication, Document De Travail Année : 2012

Spectrum of hypersurfaces with small extrinsic radius or large $\lambda_1$ in euclidean spaces

Erwann Aubry

Résumé

In this paper, we prove that Euclidean hypersurfaces with almost extremal extrinsic radius or $\lambda_1$ have a spectrum that asymptotically contains the spectrum of the extremal sphere in the Reilly or Hasanis-Koutroufiotis Inequalities. We also consider almost extremal hypersurfaces which satisfy a supplementary bound on $v_M\|\B\|_\alpha^n$ and show that their spectral and topological properties depends on the position of $\alpha$ with respect to the critical value $\dim M$. The study of the metric shape of these extremal hypersurfaces will be done in \cite{AG1}, using estimates of the present paper.
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Dates et versions

hal-00743727 , version 1 (19-10-2012)
hal-00743727 , version 2 (14-03-2017)

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Citer

Erwann Aubry, Jean-Francois Grosjean. Spectrum of hypersurfaces with small extrinsic radius or large $\lambda_1$ in euclidean spaces. 2012. ⟨hal-00743727v1⟩

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