arXiv:2610.37817v1 Announce Type: new 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.
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