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

Allan Freitas; Felippe Guimarães

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arXiv · 2404.12197

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

Allan Freitas·Felippe Guimarães

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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.

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Allan Freitas, Felippe Guimarães. 2024-04-18. A congruence theorem for compact embedded hypersurfaces in $\mathbb{S}^{n+1}_+$. https://arxiv.org/abs/2404.12197

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