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Hypersurfaces with prescribed boundary and small Steklov eigenvalues
Auteur(s)
Date de parution
2020-1-17
In
Canadian Mathematics Bulletin
No
63
De la page
46
A la page
57
Résumé
iven a smooth compact hypersurface $M$ with boundary $\Sigma=\partial M$, we prove the existence of a sequence $M_j$ of hypersurfaces with the same boundary as $M$, such that each Steklov eigenvalue $\sigma_k(M_j)$ tends to zero as $j$ tends to infinity. The hypersurfaces $M_j$ are obtained from $M$ by a local perturbation near a point of its boundary. Their volumes and diameters are arbitrarily close to those of $M$, while the principal curvatures of the boundary remain unchanged.
Identifiants
Type de publication
journal article
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