Preprint

Inserted: 30 oct 2026

Year: 2026

Abstract:

We establish the generalized Cartan-Hadamard conjecture, including rigidity in the equality case. As a corollary, we obtain that isoperimetric regions are bounded. We prove the conjecture for Alexandrov spaces with two sided curvature bounds as well. A sharp Michael-Simon-type inequality for hypersurfaces in these spaces is also shown.