Minimal hulls of compact sets in $\mathbb {R}^3$
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- by Barbara Drinovec Drnovšek and Franc Forstnerič PDF
- Trans. Amer. Math. Soc. 368 (2016), 7477-7506 Request permission
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.References
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Additional Information
- Barbara Drinovec Drnovšek
- Affiliation: Faculty of Mathematics and Physics, University of Ljubljana – and – Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI–1000 Ljubljana, Slovenia
- Email: barbara.drinovec@fmf.uni-lj.si
- Franc Forstnerič
- Affiliation: Faculty of Mathematics and Physics, University of Ljubljana – and – Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI–1000 Ljubljana, Slovenia
- MR Author ID: 228404
- Email: franc.forstneric@fmf.uni-lj.si
- Received by editor(s): October 24, 2014
- Published electronically: December 14, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7477-7506
- MSC (2010): Primary 53A10, 32U05; Secondary 32C30, 32E20, 49Q05, 49Q15
- DOI: https://doi.org/10.1090/tran/6777
- MathSciNet review: 3471098