In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application, we obtain a global existence result for the surface diffusion flow, providing that an initial curve is $$H^2$$ H 2 -close to a multiply covered circle and is sufficiently rotationally symmetric.

中文翻译：

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关于多重缠绕曲线的等周不等式和表面扩散流

在本文中，我们建立了旋转对称平面中浸入式闭合曲线（可能是非凸曲线）的等周不等式的一般形式。作为一个应用，我们获得了表面扩散流的全局存在结果，前提是初始曲线是 $$H^2$$H 2 - 接近一个多重覆盖的圆并且足够旋转对称。