Stability and area growth of $\lambda$-hypersurfaces

Abstract

In this paper, We define a $\mathcal{F}$-functional and study $\mathcal{F}$-stability of $\lambda$-hypersurfaces, which extend a result of Colding-Minicozzi. Lower bound growth and upper bound growth of area for complete and non-compact $\lambda$-hypersurfaces are studied.