Quantitative smoothing of polyhedral manifolds
Abstract
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 .
Fields of Study & Subjects
Computational Geometry and Mesh Generation
Advanced Numerical Analysis Techniques
Mathematics and Applications
Publication details
- Journal / source
- Comptes Rendus Mathématique
- Volume
- 364
- Issue
- G3
- Pages
- 583–588
- Publication date
- 1 July 2026
- Language
- EN