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arXiv · 2204.05020

On an isoperimetric problem on the Lobachevsky hyperbolic plane with left-invariant Finsler structure

Viktoria Myrikova
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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.

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Viktoria Myrikova. 2022-04-11. On an isoperimetric problem on the Lobachevsky hyperbolic plane with left-invariant Finsler structure. https://arxiv.org/abs/2204.05020

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