NEW STABILITY RESULTS FOR SPHERES AND WULFF SHAPES

Julien Roth (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove that a closed convex hypersurface of a Euclidean space with almost constant anisotropic first and second mean curvatures in the L p-sense is W 2,p-close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hypersphere of space forms improving those of [7] and [8].

Domaines: Géométrie différentielle [math.DG]

Julien Roth. NEW STABILITY RESULTS FOR SPHERES AND WULFF SHAPES. Communications in Mathematics, 2018, 26 (2), pp.153-167. ⟨hal-01228821v4⟩