English

Supersqueezed sphere

Differential Geometry 2025-11-18 v1 Geometric Topology

Abstract

This work pose an example of a smooth closed surface in R3\mathbb{R}^3 which has genus 00, normal curvatures at most 11 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.

Keywords

Cite

@article{arxiv.2511.12598,
  title  = {Supersqueezed sphere},
  author = {Hongda Qiu},
  journal= {arXiv preprint arXiv:2511.12598},
  year   = {2025}
}
R2 v1 2026-07-01T07:39:45.923Z