The isoperimetric problem is one of the fundamental problems in differential geometry. By using the method of the calculus of variations we show that the circle centered at the origin in $${\mathbb {B}}^2(1)$$ is a proper maximum of the isoperimetric problem in a 2-dimensional Finsler space of Funk type. We also obtain the formula of area enclosed by a simple closed curve in a spherically symmetric Finsler plane.

中文翻译：

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关于Funk型二维Finsler空间中的等周问题

等周问题是微分几何中的基本问题之一。通过变分法，我们证明$${\mathbb {B}}^2(1)$$中以原点为中心的圆是二维Finsler空间中等周问题的适当极大值Funk 类型。我们还获得了球对称 Finsler 平面中由简单闭合曲线包围的面积公式。