For every integer n≥2 and real κ, a complete separable metric space is an n-dimensional Alexandrov space of curvature at least κ exactly when its Hausdorff-measure metric space has full support, is RCD((n−1)κ,n), and has Gigli distributional sectional curvature at least κ on the original global test classes.
For every integer n≥2 and real κ, a complete separable metric space is an n-dimensional Alexandrov space of curvature at least κ exactly when its Hausdorff-measure metric space has full support, is RCD((n−1)κ,n), and has Gigli distributional sectional curvature at least κ on the original global test classes.
For every integer n≥2 and real κ, a complete separable metric space is an n-dimensional Alexandrov space of curvature at least κ exactly when its Hausdorff-measure metric space has full support, is RCD((n−1)κ,n), and has Gigli distributional sectional curvature at least κ on the original global test classes.
If correct, resolves Gigli’s characterization conjecture in dimensions at least two.
Does Gigli’s distributional sectional-curvature bound characterize Alexandrov lower curvature?
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OpenAI reports Gigli’s Alexandrov curvature characterization
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