Submanifolds of class $C^{1,α}$ and sets with positive $μ$-reach
Abstract
It is well-known since the seminal work of Herbert Federer [Trans. of the AMS, 1959] that submanifolds of class $C^{1,1}$ have positive reach. In this paper, we extend this property to less regular submanifolds by using the notion of $μ$-reach that was introduced in the 2000's. We first show that every compact $C^1$ submanifold of the Euclidean space $\E^n$ has positive $μ$-reach for all $μ
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint