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arXiv · 2303.15272

The Isoperimetric Problem in Randers Poincar\'e Disc

Arti Sahu Gangopadhyay·Ranadip Gangopadhyay·Hemangi Madhusudan Shah·Bankteshwar Tiwari
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Abstract

It is known that a simply connected Riemann surface satisfies the isoperimetric equality if and only if it has constant Gaussian curvature. In this article, we show that Randers Poincar\'e disc satisfies the isoperimetric equality with respect to different volume forms. These metrics do not necessarily have constant (negative) flag curvature. Thus we show that the Osserman's result \cite{RO} in the Riemannian case can not be extended to the corresponding Finslerian case.

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Arti Sahu Gangopadhyay, Ranadip Gangopadhyay, Hemangi Madhusudan Shah, Bankteshwar Tiwari. 2023-03-27. The Isoperimetric Problem in Randers Poincar\'e Disc. https://arxiv.org/abs/2303.15272

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