Metric shape of hypersurfaces with small extrinsic radius or large $   \lambda_1$
  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. 
Erwann Aubry (JAD), Jean-Francois Grosjean (IECN)
math.DG