Geodesic
Hypersurfaces with Prescribed Boundary and Small Steklov Eigenvalues
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 46-57

Voir la notice de l'article provenant de la source Cambridge University Press

Given a smooth compact hypersurface $M$ with boundary $\unicode[STIX]{x1D6F4}=\unicode[STIX]{x2202}M$, we prove the existence of a sequence $M_{j}$ of hypersurfaces with the same boundary as $M$, such that each Steklov eigenvalue $\unicode[STIX]{x1D70E}_{k}(M_{j})$ 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.
DOI : 10.4153/S000843951900050X
Mots-clés : Steklov eigenvalue, hypersurface 
Colbois, Bruno; Girouard, Alexandre; Métras, Antoine. Hypersurfaces with Prescribed Boundary and Small Steklov Eigenvalues. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 46-57. doi: 10.4153/S000843951900050X
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