A Rigidity Theorem of λ-Hypersurfaces

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.