Lorentz空间R_1^(n+1)中类空λ-超曲面的刚性定理（英文）

RIGIDITY THEOREMS OF THE SPACE-LIKEλ-HYPERSURFACES IN THE LORENTZIAN SPACE R_1^(n+1)

本文研究了Lorentz空间R_1^(n+1)中完备的类空λ-超曲面的刚性问题.利用推广了的L-算子的性质和一些积分不等式,最终得到了关于这类超曲面的若干刚性定理,其中包括R_1^(n+1)中加权的完备类空自收缩子的刚性,推广了此前欧氏空间完备λ-超曲面的相关结果.

In this paper, we study complete space-like λ-hypersurfaces in the Lorentzian space R1 n＋1. By using the property of generalized ^-operator and some integral inequalities, we obtain some rigidity theorems for these hypersurfaces including the complete space-like self-shrinkers with weight in R1n＋1 , which generalize some related results in the Euclidean space.