# The isoperimetric problem in the 2-dimensional Finsler space forms with k = 0. I

## TL;DR

This paper investigates the isoperimetric problem in 2D Finsler space forms with zero curvature, demonstrating that the circle centered at the origin maximizes the Busemann-Hausdorff area locally.

## Contribution

It provides a proof that the centered circle is a local maximizer for the isoperimetric problem in this specific Finsler setting.

## Key findings

- Centered circle maximizes the Busemann-Hausdorff area locally
- The isoperimetric problem is analyzed in 2D Finsler space forms with zero curvature
- The circle achieves a local maximum area in this geometric context

## Abstract

In this paper, the isoperimetric problem in the 2-dimensional Finsler space form $(F_B,B^2(1))$ with k = 0 by using the Busemann-Hausdorff area is investigated. We prove that the circle centered the origin achieves the local maximum area of the isoperimetric problem.