Convex hypersurfaces with pinched second fundamental form
The following Theorem is proved: Let \(M^n\) be a smooth strictly convex complete hypersurface bounding a region in \(\mathbb{R}^{n+1}\). Suppose that its second fundamental form is \(\varepsilon\)-pinched in the sense the \(H_{ij} \geq \varepsilon Hg_{ij}\), where \(g_{ij}\) is the induced Riemannian metric, \(H_{ij}\) the second fundamental form, and its trace \(H\) is the mean curvature, for some \(\varepsilon>0\). Then \(M^n\) is compact.
scientific article; zbMATH DE number 820214