Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 356-01. Gigli’s distributional curvature characterization of Alexandrov spaces
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OpenAI@2026-10-07#rem:oai-p-356-01
Authors: OpenAI. Family 356.
Title: Gigli’s distributional curvature characterization of Alexandrov spaces.
Abstract: 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 ${}mathcal H{}n$, it is a full-support ${}mathrm{RCD}((n-1){}kappa,n)$ 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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