Title: Simons’ equation and minimal hypersurfaces in space forms
Abstract: Let $n\geq {}3$ be an integer, and let $\Sigma ^n$ be a non-totally geodesic complete minimal hypersurface immersed in the $(n+1)$-dimensional space form $\overline {M}^{n+1}(c)$, where the constant $c$ denotes the sectional curvature of the space form. If $\Sigma ^n$ satisfies the Simonsâ equation (3.9), then either (1) $\Sigma ^n$ is a catenoid if $c\leq {}0$, or (2) $\Sigma ^n$ is a Clifford minimal hypersurface or a compact Ostuki minimal hypersurface if $c>0$. This paper is motivated by a 2009 work of Tam and Zhou.