Geometry and topology · Oct 6, 2026

Gigli’s characterization of Alexandrov curvature

Proves Gigli's conjecture: in every integer dimension n ≥ 2, Alexandrov curvature at least κ is characterized by the full-support

\mathop{\mathrm{RCD}}\nolimits ((n-1)\kappa,n)

condition with reference measure

\mathcal H^n

and distributional sectional curvature at least κ in the original global test classes. The RCD condition is unreduced.

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