On an isoperimetric problem on the Lobachevsky hyperbolic plane with left-invariant Finsler structure
Differential Geometry
2023-01-10 v2 Optimization and Control
Abstract
We deal with an isoperimetric problem on the Finsler hyperbolic plane. The space is defined as the Lie group of proper affine transformations of the line with a left-invariant Finsler structure. To state the problem, we use the left-invariant volume form. The optimal isoperimetric loops are found in terms of convex trigonometry functions. We also propose a generalization of the isoperimetric inequality in parametric form.
Keywords
Cite
@article{arxiv.2204.05020,
title = {On an isoperimetric problem on the Lobachevsky hyperbolic plane with left-invariant Finsler structure},
author = {Viktoria Myrikova},
journal= {arXiv preprint arXiv:2204.05020},
year = {2023}
}
Comments
17 pages, 2 figures, in Russian