Minimal hulls of compact sets in ${\mathbb{R}}^3$

Abstract

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.

Trans. Amer. Math. Soc., in press. The official version is available at http://dx.doi.org/10.1090/tran/6777

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