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

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DOI

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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     title = {Hypersurfaces with {Prescribed} {Boundary} and {Small} {Steklov} {Eigenvalues}},
     journal = {Canadian mathematical bulletin},
     pages = {46--57},
     year = {2020},
     volume = {63},
     number = {1},
     doi = {10.4153/S000843951900050X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843951900050X/}
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