A congruence theorem for compact embedded hypersurfaces in ${\mathbb{S}}_{+}^{n+1}$

Allan Freitas, Felippe Guimarães

We prove a codimension reduction and congruence theorem for compact $n$-dimensional submanifolds of ${\mathbb{S}}^{n+p}$ that admit a mean convex isometric embedding into $\mathbb{S}…