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

Abstract

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 ${\mathbb{S}}_{+}^{n+1}$ using a Reilly type formula for space forms.

Minor changes. To appear in Bulletin of the London Mathematical Society