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

TL;DR

This paper studies the isoperimetric problem in 2D Finsler space forms with zero curvature, showing that the circle centered at the origin maximizes the Holmes-Thompson area locally.

Contribution

It extends previous work by proving the circle centered at the origin locally maximizes area in the Finsler space form with k=0 using Holmes-Thompson area.

Findings

Circle centered at the origin achieves local maximum area.

The study focuses on Finsler space forms with zero curvature.

Uses Holmes-Thompson area measure.

Abstract

This paper is a continuation of the second author's previous work. We investigate the isoperimetric problem in the 2-dimensional Finsler space form $(F_B, B^2(1))$ with $k=0$ by using the Holmes-Thompson area and prove that the circle centered the origin achieves the local maximum area of the isoperimetric problem.