11 citations · 20 across the 9 of their papers we have counts for
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Reilly inequality for Varifolds
Jean-François Grosjean, Antoine Lemenant, Rémy Mougenot
The famous Reilly inequality gives an upper bound for the first eigenvalue of the Laplacian defined on compact submanifolds of the Euclidean space in terms of the -norm of the…
On the boundary of almost isoperimetric domains
Erwann Aubry, Jean-François Grosjean
We prove that finite perimeter subsets of with small isoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset of small measure. We also ref…
Spectrum of hypersurfaces with small extrinsic radius or large in euclidean spaces
Erwann Aubry, Jean-Francois Grosjean
In this paper, we prove that Euclidean hypersurfaces with almost extremal extrinsic radius or have a spectrum that asymptotically contains the spectrum of the extremal sphere…
Metric shape of hypersurfaces with small extrinsic radius or large
Erwann Aubry, Jean-Francois Grosjean
We determine the Hausdorff limit-set of the Euclidean hypersurfaces with large or small extrinsic radius. The result depends on the norm of the curvature that is assume…
Almost harmonic spinors
Nicolas Ginoux, Jean-François Grosjean
We show that any closed spin manifold not diffeomorphic to the two-sphere admits a sequence of volume-one-Riemannian metrics for which the smallest non-zero Dirac eigenvalue tends…
Hypersurfaces with small extrinsic radius or large in Euclidean spaces
Erwann Aubry, Jean-Francois Grosjean, Julien Roth
We prove that hypersurfaces of which are almost extremal for the Reilly inequality on and have -bounded mean curvature () are Hausdorff close to a sphere…