2024/10/01 by Arti Sahu Gangopadhyay, Ranadip Gangopadhyay, Hemangi Madhusudan Shah +1
Physics and Astronomy · #Advanced Differential Geometry Research
paper · doi:10.5486/pmd.2024.9705
crossref issued 2024/10/01 · crossref published 2024/10/01 · crossref published-online 2024/10/01 · openalex publication_date 2024/10/01 · crossref created 2024/10/10 · crossref deposited 2025/02/27 · openalex created_date 2025/10/10 · crossref indexed 2026/07/25 · openalex updated_date 2026/07/26
In 1947, Busemann observed that a Minkowski circle need not be a solution of the isoperimetric problem in a Minkowski plane. Li and Mo recently showed that the Euclidean circles centred at the origin in a unit ball with the Funk metric are solutions of the isoperimetric problem [9]. In this paper, we construct a class of Randers planes in which any Euclidean circle, centered at the origin in ℝ2, turns out to be a local minimum of the isoperimetric problem with respect to the various well-known volume forms in Finsler geometry. As a consequence, it turns out that the Euclidean circles centred at the origin are solutions of the isoperimetric problem in a Randers type Minkowski plane.