Abstract
It is shown that embedded, elliptic $r$-minimal hypersurfaces in Euclidean space $\mathbb{R}^{n+1}$, $\frac{3}{2}(r+1)\leq n<2(r+1)$, with two ends, both regular, are catenoids (i.e., rotational hypersurfaces). This extends to this setting previous results by Schoen and Hounie-Leite.
Citation
Levi Lopes de Lima. Antonio Sousa. "Two-ended $r$-minimal hypersurfaces in Euclidean space." Illinois J. Math. 55 (4) 1327 - 1348, Winter 2011. https://doi.org/10.1215/ijm/1373636686
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