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arXiv · 1210.5690

Spectrum of hypersurfaces with small extrinsic radius or large $λ_1$ in euclidean spaces

Erwann Aubry·Jean-Francois Grosjean
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Abstract

In this paper, we prove that Euclidean hypersurfaces with almost extremal extrinsic radius or $λ_1$ 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 $v_M\|\B\|_α^n$ and show that their spectral and topological properties depends on the position of $α$ 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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Erwann Aubry, Jean-Francois Grosjean. 2012-10-21. Spectrum of hypersurfaces with small extrinsic radius or large $λ_1$ in euclidean spaces. https://arxiv.org/abs/1210.5690

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