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arXiv · 1905.08532

Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface system

Xiaowei Xu·Ling Yang·Yongsheng Zhang
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Abstract

We make systematic developments on Lawson-Osserman constructions relating to the Dirichlet problem (over unit disks) for minimal surfaces of high codimension in their 1977 Acta paper. In particular, we show the existence of boundary functions for which infinitely many analytic solutions and at least one nonsmooth Lipschitz solution exist simultaneously. This newly-discovered amusing phenomenon enriches the understanding on the Lawson-Osserman philosophy.

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Xiaowei Xu, Ling Yang, Yongsheng Zhang. 2019-05-21. Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface system. https://arxiv.org/abs/1905.08532

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