A global pinching theorem of complete $\lambda$-hypersurfaces

In this paper, the pinching problems of complete $\lambda$-hypersurfaces in a Euclidean space ${\mathbb{R}}^{n+1}$ are studied. By making use of the Sobolev inequality, we prove a global pinching theorem of complete $\lambda$-hypersurfaces in a Euclidean space ${\mathbb{R}}^{n+1}$.