article

Title: Two-ended hypersurfaces with $H_r=0$

Authors: Henrique Araujo and Maria Luiza Leite

Issue: Volume 61 (2012), Issue 4, 1667-1693

Abstract:

$We show that an embedded hypersurface in $\mathbb{R}^{n+1}$ with vanishing $r$-mean curvature $H_r$ and regular at infinity with two ends must be rotational, provided $H_{r+1}$ never vanishes, $1 < r < n$. This extends previously known results for $r = 2$ and $n/2 < r leq 2n/3$. The minimal case was established by R. Schoen for immersions, without any assumption on $H_2$.$