The Isoperimetric Problem in Randers Poincar\'e Disc
Differential Geometry
2023-03-28 v1
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.
Keywords
Cite
@article{arxiv.2303.15272,
title = {The Isoperimetric Problem in Randers Poincar\'e Disc},
author = {Arti Sahu Gangopadhyay and Ranadip Gangopadhyay and Hemangi Madhusudan Shah and Bankteshwar Tiwari},
journal= {arXiv preprint arXiv:2303.15272},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2204.00760