<i>λ</i>-超曲面的一个积分等式

λ-超曲面的一个积分等式

摘要: 研究了λ-超曲面，得到了有关完备的λ-超曲面的一个积分等式：若 X :M→\mathbbRⁿ⁺¹是n-维完备的具有多项式面积增长的λ-超曲面且满足S有界，则有∫_M(|▽H|²+(H-λ)(H+S(λ-H)))\rme^ - \frac|\mathit\boldsymbolX|^22dμ=0，其中，H是M的平均曲率，S是M的第二基本形式模长平方.并由该积分等式得到了一个刚性结果.

Abstract: λ-hypersurfaces are studied and a rigidity result about complete λ-hypersurfaces is given. If X :M→\mathbbRⁿ⁺¹ is an n-dimensional complete λ-hypersurface with polynomial area growth and satisfies S bounded, then ∫_M(|▽H|²+(H-λ)(H+S(λ-H)))\rme^ - \frac|\mathit\boldsymbolX|^22dμ=0, where H is the mean curvature of M, S is the squared norm of the second fundamental form of M. As an application of the integral equation, a rigidity result about complete λ-hypersurfaces is obtained.