Rigidity theorems of $λ$-hypersurfaces
Rigidity theorems of $λ$-hypersurfaces
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发表时间：
2014-03
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通讯作者：
Q. Cheng;S. Ogata;G. Wei
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作者：
Q. Cheng;S. Ogata;G. Wei
由于欧氏空间R中的n维λ-超曲面是加权保体积变分的加权面积泛函的临界点，本文研究了完备λ-超曲面的刚性性质.给出了多项式面积增长的完备λ-超曲面的间隙定理。利用λ-超曲面L的广义极大值原理，证明了完备λ-超曲面的一个刚性定理.
Since n-dimensional λ-hypersurfaces in the Euclidean space R are critical points of the weighted area functional for the weighted volume-preserving variations, in this paper, we study the rigidity properties of complete λ-hypersurfaces. We give some gap theorems of complete λ-hypersurfaces with polynomial area growth. By making use of the generalized maximum principle for L of λ-hypersurfaces, we prove a rigidity theorem of complete λhypersurfaces.