The Isoperimetric Problem In Randers Planes

The Isoperimetric Problem In Randers Planes

In this paper, the isoperimetric problem in Randers planes, \((\mathbb{R}^2,F=\alpha +\beta)\), which are slight deformation of the Euclidean plane \((\mathbb{R}^2,\alpha)\) by suitable one forms \(\beta\), have been studied. We prove that the circles centred at the origin achieves the local maximum...

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Veröffentlicht in:arXiv.org 2022-04
Hauptverfasser: Sahu, Arti, Gangopadhyay, Ranadip, Shah, Hemangi Madhusudan, Tiwari, Bankteshwar
Format: Artikel
Sprache:eng
Schlagworte:
Euclidean geometry
Isoperimetric problem
Planes
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Zusammenfassung:In this paper, the isoperimetric problem in Randers planes, \((\mathbb{R}^2,F=\alpha +\beta)\), which are slight deformation of the Euclidean plane \((\mathbb{R}^2,\alpha)\) by suitable one forms \(\beta\), have been studied. We prove that the circles centred at the origin achieves the local maximum area of the isoperimetric problem with respect to well known volume forms in Finsler geometry.
ISSN:2331-8422