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arXiv · 1704.07869

On a free boundary problem and minimal surfaces

Yong Liu·Kelei Wang·Juncheng Wei
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Abstract

From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension $8$, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that Savin's theorem is optimal.

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Yong Liu, Kelei Wang, Juncheng Wei. 2017-04-25. On a free boundary problem and minimal surfaces. https://arxiv.org/abs/1704.07869

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