357. Bi-Lipschitz coordinates at every regular RCD point

Bi-Lipschitz coordinates at every regular RCD point

1 paper

Proves that every regular point of a noncollapsed \(\mathop{\mathrm{RCD}}\nolimits (K,n)\) space, for K ∈ ℝ and integer n ≥ 2, has an open neighborhood bi-Lipschitz to an open subset of ℝⁿ. Regularity requires all pointed tangents to be Euclidean, the reference measure is exactly \(\mathcal H^n\), and the chart compares ambient distances with a point-dependent finite constant.

Papers 1

Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces

OpenAI · September 25, 2026

We resolve the regular-point bi-Lipschitz conjecture in the noncollapsed setting. For every integer n ≥ 2 and every real K, every regular point of a noncollapsed \(\mathrm{RCD}(K,n)\) space has an open neighborhood bi-Lipschitz homeomorphic to an open subset of ℝⁿ. The bi-Lipschitz constant depends only on n, and the neighborhood uses the restricted ambient distance.

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@misc{OAI:Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026,
  author = {{OpenAI}},
  title = {{Bi-Lipschitz Coordinates at Regular Points of Noncollapsed $\mathrm{RCD}$ Spaces}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026/paper.pdf}{OAI:Bi-Lipschitz-Coordinates-at-Regular-Points-of-Noncollapsed-RCD-Spaces-September-25-2026}},
  year = {2026}
}

Bi-Lipschitz coordinates at every regular RCD point

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Papers 1

Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces

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