Bi-Lipschitz coordinates at every regular RCD point. 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.
released 2026-09-25 | 1 theorem · 22 lemmas · 27 proofs · 17,722 words |
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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.