Quantitative smoothing of polyhedral manifolds
Spencer Cattalani · Comptes Rendus Mathématique · 2026
We use a recent result of C. Lange to obtain a converse to a theorem of B. Bowditch in dimension at most 4 . In particular, we show that, for n ≤ 4 , a polyhedral n -manifold X with bounded geometry is K -bi-Lipschitz homeomorphic to a Riemannian manifold M . We bound the constant K , the curvature, and the injectivity radius of M by the bounds on the geometry of X .