Family 357Differential geometryNo LeanNot yet digested
Bi-Lipschitz coordinates at every regular RCD point
Proves that every regular point of a noncollapsed space, for K ∈ ℝ and integer n ≥ 2, has an open neighborhood bi-Lipschitz to an open subset of ℝ. Regularity requires all pointed tangents to be Euclidean, the reference measure is exactly , and the chart compares ambient distances with a point-dependent finite constant.
Manuscripts in this family · 1
Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces
Sep 25, 2026·paper.pdf
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 space has an open neighborhood bi-Lipschitz homeomorphic to an open subset of ℝ. The bi-Lipschitz constant depends only on n, and the neighborhood uses the restricted ambient distance.