Supersqueezed sphere

2025/11/16 by Qiu, Hongda · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2511.12598

Abstract

This work pose an example of a smooth closed surface in ℝ³ 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.

Citations

• Extremal problems for surfaces of prescribed topological type (1)

Cited by

• A genus-zero surface with bounded curvature enclosing less volume than the unit sphere

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