English

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}
}
R2 v1 2026-06-28T12:50:12.092Z