On the curvature bounded sphere problem in $$\mathbb {R}^3$$
Abstract
Abstract Let $$S\subset \mathbb {R}^3$$ S ⊂ R 3 be a smooth embedded sphere whose normal curvatures have absolute value at most 1. We prove that if S is contained in an open ball of radius 2, then the body bounded by S contains a unit ball.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Point processes and geometric inequalities
Publication details
- Journal / source
- Geometriae Dedicata
- Publisher
- Springer Science and Business Media LLC
- Volume
- 220
- Issue
- 4
- Publication date
- 1 August 2026
- Language
- EN