Helicoids and vortices

arxiv(2022)

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摘要
We point out an interesting connection between fluid dynamics and minimal surface theory: When gluing helicoids into a minimal surface, the limit positions of the helicoids correspond to a "vortex crystal", an equilibrium of point vortices in 2D fluid that move together as a rigid body. While vortex crystals have been studied for almost 150 years, the gluing construction of minimal surfaces is relatively new. As a consequence of the connection, we obtain many new minimal surfaces and some new vortex crystals by simply comparing notes.
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关键词
minimal surfaces,vortex dynamics,gluing construction
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