Authors: Julien Roth ^1,2

• 1 Laboratoire Analyse et Mathématiques Appliquées [LAMA]
• 2 Laboratoire Analyse et de Mathématiques Appliquées [LAMA]

We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the Lp -sense is W 2 ,p -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [10] and [11].