We show that the spectrum of the relativistic mean curvature operator on a bounded domain Ω ⊂ ℝN (N ⩾ 1) having smooth boundary, subject to the homogeneous Dirichlet boundary condition, is exactly the interval (λ1(2), ∞), where λ1(2) stands for the principal frequency of the Laplace operator in Ω.

中文翻译：

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平均曲率算子的谱

我们证明了有界域 Ω ⊂ ℝ 上的相对论平均曲率算子的谱ñ(ñ⩾ 1) 具有光滑边界，服从齐次狄利克雷边界条件，恰好是区间 (λ1(2), ∞), 其中 λ1(2) 代表拉普拉斯算子的主频率Ω.