Two moons in a puddle
Differential Geometry
2025-12-08 v1
Abstract
We prove that a simple closed plane curve with curvature at most 1 and diameter at least 4, surrounds two disjoint open unit disks. We also pose an open question relating the diameter lower bound to the length of the curve.
Cite
@article{arxiv.2310.09301,
title = {Two moons in a puddle},
author = {Berk Ceylan},
journal= {arXiv preprint arXiv:2310.09301},
year = {2025}
}