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arXiv · 2511.12598

Supersqueezed sphere

Hongda Qiu
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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.

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Hongda Qiu. 2025-11-16. Supersqueezed sphere. https://arxiv.org/abs/2511.12598

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