On Gromov's flat corner domination conjecture and Stoker's conjecture

TL;DR

This paper proves Gromov's flat corner domination conjecture across all dimensions, confirming Stoker's conjecture for convex Euclidean polyhedra, and establishes a rigidity theorem for strictly convex domains in Euclidean spaces.

Contribution

It provides a complete proof of Gromov's conjecture in all dimensions and confirms Stoker's conjecture for convex polyhedra, introducing new techniques for rigidity in convex geometry.

Findings

Gromov's flat corner domination conjecture proven in all dimensions

Stoker's conjecture confirmed for convex Euclidean polyhedra

A new rigidity theorem for strictly convex domains

Abstract

In this paper, we prove Gromov's flat corner domination conjecture in all dimensions. As a consequence, we answer positively the Stoker conjecture for convex Euclidean polyhedra in all dimensions. By applying the same techniques, we also prove a rigidity theorem for strictly convex domains in Euclidean spaces.