2025/04/03 by Alexander Thomas, Thomas, Alexander
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2504.02907
openalex publication_date 2025/04/03 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28
We explore convex shapes S in the Euclidean plane which have the following property: there is a circle C such that the angle between the two tangents from any point of C to S is constant equal to α. A dynamical formulation allows to analyze the existence of such shapes. Interestingly, the existence of non-circular shapes depends in a non-trivial way on the angle α.