Family 356Differential geometryLeanNot yet digested
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 condition with reference measure and distributional sectional curvature at least κ in the original global test classes. The RCD condition is unreduced.
Manuscripts in this family · 2
Gigli’s distributional curvature characterization of Alexandrov spaces
Sep 24, 2026·main.pdf
For every integer n ≥ 2 and κ ∈ ℝ, we prove that a complete separable metric space is an n-dimensional Alexandrov space of curvature at least κ if and only if, with reference measure , it is a full-support space whose distributional sectional curvature is at least κ in Gigli's original global test classes. This resolves Gigli's characterization conjecture in dimensions at least two.
Weak Hessian bounds along every geodesic in RCD spaces
Sep 24, 2026·weak-hessian-geodesics.pdfLean
On a full-support space with , we prove that a bounded globally Lipschitz function whose distributional Hessian is bounded above by a bounded continuous function satisfies the corresponding second-derivative inequality along every minimizing geodesic.