The generalized Cartan-Hadamard conjecture compares isoperimetric profiles of complete simply connected Riemannian
manifolds with an upper bound on sectional
curvature. If 
, the proposed inequality is
 |
where 
is the infimum of perimeters of finite
perimeter sets of volume 
in the 
-dimensional manifold 
, and 
is the complete simply
connected model of constant curvature 
. The case 
is the Cartan-Hadamard conjecture, which gives the Euclidean
isoperimetric inequality (Ghomi and Spruck
2022).
Agnoletto et al. (2026) reported the inequality in all dimensions, without an additional global lower Ricci-curvature bound in the smooth theorem. They also report that equality for a positive-volume finite perimeter set forces it to agree, up to a set of volume zero, with a region isometric to a model geodesic ball. Their treatment adapts analytic techniques from an earlier OpenAI manuscript and requires independent assessment. Agnoletto et al. (2026) report mathematical assistance from Claude and ChatGPT.
