Title: Rigidity of complete self-shrinkers whose tangent planes omit a nonempty set

Abstract: In this paper we prove rigidity results for the sphere, the plane and the right circular cylinder as the only self-shrinkers satisfying a classic geometric assumption, namely the union of all tangent affine submanifolds of a complete self-shrinker omits a non-empty set of the Euclidean space. This assumption lead us to a new class of submanifolds, different from those with polynomial volume growth or the proper ones. We also prove an analogous result for self-expanders.