https://neckpinch.com/authors/shaosai-huang/New arXiv papers by Shaosai Huang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.17229/arxiv:2610.17229Mon, 12 Oct 2026 00:00:00 GMTShaosai Huang — Let compact RCD(κ,N) spaces converge in the measured Gromov–Hausdorff sense, and suppose that they have (δ,ρ)-Reifenberg local covers for one fixed ρ>0, with |κ|ρ²≤1 and δ small. We prove that, along a subsequence, the spaces are singular fibrations over the limit: their canonical frame spaces converge to a topological manifold with a locally linear action of O(n) whose quotient is the limit; for large indices the frame spaces fibre over this manifold, by maps that commute with O(n), with fibres homeomorphic to nilmanifolds; and the induced maps to the limit are, near every point, quotients of products by the isotropy group, with fibres homeomorphic to infranilmanifolds. As applications, we extend a fibration theorem of Honda and Zhang to non-smooth RCD spaces whose local covers have injectivity radius bounded below, and we show that for aspherical spaces the isotropy groups are finite, the fibre groups inject into the fundamental groups, and the limit is the quotient of a contractible manifold by a proper cocompact action; under Rong's condition Aₛ it is a closed aspherical manifold. Three appendices treat smooth manifolds with Ric≥−(n-1) and small local rewinding Reifenberg error: a uniform short-time Ricci flow with |Rm|≤α/t, also for complete non-compact data, where it is unique among complete flows with curvature at most A/t; a second construction with affine nilmanifold bundles; and, conditional on Nifa's construction, examples showing that rewinding volume control alone does not give continuous Gromov–Hausdorff approximations with small error.Ricci flow(Non)collapsingWeak & singular flowsLimit spaces & RCDHomogeneous spacesBoundaries & non-compact