Spectral properties of constant mean curvature submanifolds in hyperbolic space
The author studies the essential spectrum of the Laplacian \(\Delta\) and of the stability operator \(S\) on hypersurfaces with constant mean curvature in hyperbolic space. He proves the following: Theorem. Let \(i: M^n\hookrightarrow H^{n+1}\) be an immersion with constant mean curvature \(h<1\). If the total curvature is finite, then \[ \sigma_{\text{ess}}(\Delta)\in \Biggl[{(n- 1)^2\over 4}(1- h^2),+\infty\Biggr) \quad\text{and} \quad\sigma_{\text{ess}}(S)\in \Biggl[{(n+ 1)^2\over 4} (1- h^2),+\infty\Biggr). \]
hypersurfaces with constant mean curvature
scientific article; zbMATH DE number 1396331