2023/10/09 by Berk Ceylan, Ceylan, Berk
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics #Curvature #Differential Geometry (math.DG) #Disjoint sets #FOS: Mathematics #Geometry #Jordan curve theorem #Mathematics #Mathematics and Applications #Philosophy #Physics #Plane (geometry) #Point processes and geometric inequalities #Simple (philosophy) #Unit (ring theory)
paper · pdf · doi:10.48550/arxiv.2310.09301
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.