$\mathbb R^3$中紧集的极小壳
Minimal hulls of compact sets in $\mathbb R^3$
摘要：
本文的主要结果是在$\mathbb R^3$中的紧集$K$的极小曲面壳的一个特征，它是由其边界在测度论意义下收敛于$K$的共形最小圆盘序列，以及由共形最小圆盘支持的格林流的极限--$2$维最小流.对于$\mathbb C^3$的紧致子集的零壳也得到了类似的结果。我们还证明了一个空壳类似的亚历山大-Stolzenberg-Wermer定理的多项式壳紧集的有限线性措施，和一个多项式壳版本的经典Bochner管定理。
英文摘要：
The main result of this paper is a characterization of the minimal surface hull of a compact set $K$ in $\mathbb R^3$ by sequences of conformal minimal discs whose boundaries converge to $K$ in the measure theoretic sense, and also by $2$-dimensional minimal currents which are limits of Green currents supported by conformal minimal discs. Analogous results are obtained for the null hull of a compact subset of $\mathbb C^3$. We also prove a null hull analogue of the Alexander-Stolzenberg-Wermer theorem on polynomial hulls of compact sets of finite linear measure, and a polynomial hull version of classical Bochner's tube theorem.
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