A Supersqueezed Sphere
Abstract
This work pose an example of a smooth closed surface in $\mathbb{R}^3$ which has genus $0$, normal curvatures at most $1$ in absolute value and encloses a volume smaller than the volume of a unit ball. It gives a negative answer to a question asked by Dmitri Burago and Anton Petrunin.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometric and Algebraic Topology
Holomorphic and Operator Theory
Publication details
- Journal / source
- The Mathematical Intelligencer
- Publication date
- 11 June 2026
- Language
- EN