Two-ended hypersurfaces with $H_r=0$ Henrique AraujoMaria Luiza Leite 53C4253C40r-mean curvatureflux formulareflection method 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 $H_2$. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.5066 10.1512/iumj.2012.61.5066 en Indiana Univ. Math. J. 61 (2012) 1667 - 1693 state-of-the-art mathematics http://iumj.org/access/