Two-ended \(r\)-minimal hypersurfaces in Euclidean space (Q358924)

This paper is destined to study embedded, elliptic \(r\)-minimal hypersurfces in Euclidean space \(\mathbb{R}^{n+1}\), known as catenoids (i.e. rotationally invariant \(r\)-minimal hypersurfaces). The work contains the following sections: preliminary results, regular \(r\)-minimal ends (a description of catenoids, regular \(r\)-minimal ends, the Newton tensor of a regular end, the flux of regular ends), and the demonstration for the followingNEWLINENEWLINE Theorem: Let \(M\subset\mathbb{R}^{n+1}\) be a complete, embedded and elliptic \(r\)-minimal hypersurface with \({3\over 2}(r+1)\leq n< 2(r+1)\). If \(M\) has two ends, both regular, then \(M\) is a catenoid.NEWLINENEWLINENEWLINEThe authors give a rigorous and clear exposition.