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Helly-type Theorems for Plane Convex Curves

2000/10/31 by Alexander Getmanenko, Getmanenko, Alexander
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG

paper · pdf · doi:10.48550/arxiv.math/0010311

6 pages, Latex

arxiv created 2000/10/31 · openalex publication_date 2000/10/31 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Families of translates and homothets of strictly convex curves are proven to possess Helly-type properties generalizing those of a circle. Weaker results are shown for arbitrary convex curves.

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