Hipersuperfícies r-mínimas com dois fins regulares

Abstract

Let Mn be a r-minimal hypersurface in R n+1, i.e., suppose M has curvature S r+1 identically zero. M is said regular if out of any compact M is the disjunct union of a finite number of ends, each regular, i.e., with the same assymptotic behavior that a rotational hypersurface. It is shown that embedded, elliptic rminimal hypersurfaces in Euclidean space Rn+1,3/2(r + 1) ≤ n < 2(r + 1), with two ends, both regular, are catenoids (i.e. rotational hypersurfaces). This extends previous results by Schoen [7] and Hounie-Leite [3].