Flexible domains for minimal surfaces in Euclidean spaces
| Autor: | Drnovsek, Barbara Drinovec, Forstneric, Franc |
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| Rok vydání: | 2022 |
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| Zdroj: | J. Math. Anal. Appl., 517(2):126653, 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2022.126653 |
| Popis: | In this paper we introduce and investigate a new notion of flexibility for domains in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ in terms of minimal surfaces which they contain. A domain $\Omega$ in $\mathbb R^n$ is said to be flexible if every conformal minimal immersion $U\to\Omega$ from a Runge domain $U$ in an open conformal surface $M$ can be approximated uniformly on compacts, with interpolation on any given finite set, by conformal minimal immersion $M\to \Omega$. Together with hyperbolicity phenomena considered in recent works, this extends the dichotomy between flexibility and rigidity from complex analysis to minimal surface theory. Comment: J. Math. Anal. Appl., to appear. https://www.sciencedirect.com/science/article/pii/S0022247X22006679 |
| Databáze: | arXiv |
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