The volume conjecture for polyhedra implies the Stoker conjecture

Giulio Belletti

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arXiv · 2209.13439

The volume conjecture for polyhedra implies the Stoker conjecture

Giulio Belletti

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Abstract

We show that the Volume Conjecture for polyhedra implies a weak version of the Stoker Conjecture; in turn we prove that this weak version of the Stoker conjecture implies the Stoker conjecture. The main tool used is an extension of a result of Montcouquiol and Weiss, saying that dihedral angles are local coordinates for compact polyhedra with angles $\leq \pi$.

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Giulio Belletti. 2022-09-27. The volume conjecture for polyhedra implies the Stoker conjecture. https://arxiv.org/abs/2209.13439

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