On the asymptotic Plateau problem for area minimizing surfaces in $${\mathbb {E}}(-1,\tau )$$
| Autor: | Patrícia Klaser, Álvaro K. Ramos, Ana Menezes |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Surface (mathematics) Pure mathematics 010102 general mathematics Boundary (topology) 01 natural sciences Plateau's problem Differential geometry 0103 physical sciences Homogeneous space 010307 mathematical physics Geometry and Topology 0101 mathematics 53A10 (Primary) 53C42 (Secondary) Analysis Mathematics |
| Zdroj: | Annals of Global Analysis and Geometry. 58:1-17 |
| ISSN: | 1572-9060 0232-704X |
| DOI: | 10.1007/s10455-020-09713-w |
| Popis: | We prove some existence and non-existence results for complete area minimizing surfaces in the homogeneous space $\mathbb{E}(-1,\tau)$. As one of our main results, we present sufficient conditions for a curve $\Gamma$ in $\partial_{\infty} \mathbb{E}(-1,\tau)$ to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in $\mathbb{E}(-1,\tau)$ having $\Gamma$ as its asymptotic boundary. Comment: Final version, accepted for publication on Ann. Global Anal. Geom. 19 pages, 6 figures |
| Databáze: | OpenAIRE |
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