{"id":"openai-math/Giglis-distributional-curvature-characterization-of-Alexandrov-spaces","pdf":"https://github.com/openai/math/blob/main/preprints/Giglis-distributional-curvature-characterization-of-Alexandrov-spaces-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Giglis-distributional-curvature-characterization-of-Alexandrov-spaces-September-24-2026","tags":["metric-geometry","alexandrov-spaces","rcd-spaces","curvature"],"score":0,"title":"Gigli’s distributional curvature characterization of Alexandrov spaces","domain":"Differential geometry","family":"356","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Gigli’s characterization of Alexandrov curvature"}