Rigidity theorems of lambda-hypersurfaces

摘要

Since n-dimensional lambda-hypersurfaces in the Euclidean space Rn+1 are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of complete lambda-hypersurfaces. We give some gap theorems of complete lambda-hypersurfaces with polynomial area growth. By making use of the generalized maximum principle for L of lambda-hypersurfaces, we prove a rigidity theorem of complete lambda-hypersurfaces.