Metric shape of hypersurfaces with small extrinsic radius or large $ \lambda_1$

Erwann Aubry (1) , Jean-Francois Grosjean (2)

1 Géométrie et Analyse
2 IECN - Institut Élie Cartan de Nancy

We determine the Hausdorff limit-set of the Euclidean hypersurfaces with large $\lambda_1$ or small extrinsic radius. The result depends on the $L^p$ norm of the curvature that is assumed to be bounded a priori, with a critical behaviour for $p$ equal to the dimension minus $1$.

Mots clés: Mean curvature; Reilly inequality; Laplacian; Spectrum; pinching results; hypersurfaces

Domaines: Géométrie différentielle [math.DG]

Erwann Aubry, Jean-Francois Grosjean. Metric shape of hypersurfaces with small extrinsic radius or large $ \lambda_1$. 2012. ⟨hal-00743723⟩