On the Isoperimetric Inequality and Surface Diffusion Flow for Multiply Winding Curves
On the Isoperimetric Inequality and Surface Diffusion Flow for Multiply Winding Curves
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DOI：
10.1007/s00205-020-01591-7
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发表时间：
2019-09
影响因子：
2.5
通讯作者：
Tatsuya Miura;S. Okabe
中科院分区：
文献类型：
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作者：
Tatsuya Miura;S. Okabe
在旋转对称条件下，我们建立了平面上浸入封闭曲线（可能是非凸曲线）的等周不等式的一般形式。作为应用，我们得到了表面扩散流的一个全局存在性结果，条件是初始曲线接近于一个复盖圆并且足够旋转对称。
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-close to a multiply covered circle and is sufficiently rotationally symmetric.