The geometry of stable minimal surfaces in metric Lie groups Article Swipe
William H. Meeks
,
Pablo Mira
,
Joaquín Pérez
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1090/tran/7634
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.1090/tran/7634
We study geometric properties of compact stable minimal surfaces with boundary in homogeneous 3-manifolds $X$ that can be expressed as a semidirect product of $\mathbb {R}^2$ with $\mathbb {R}$ endowed with a left invariant metric. For any such compact minimal surface $M$, we provide an a priori radius estimate which depends only on the maximum distance of points of the boundary $\partial M$ to a vertical geodesic of $X$. We also give a generalization of the classical Radó theorem in $\mathbb {R}^3$ to the context of compact minimal surfaces with graphical boundary over a convex horizontal domain in $X$, and we study the geometry, existence, and uniqueness of this type of Plateau problem.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1090/tran/7634
- https://www.ams.org/tran/2019-372-02/S0002-9947-2019-07634-1/S0002-9947-2019-07634-1.pdf
- OA Status
- bronze
- Cited By
- 5
- References
- 31
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2539939190
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https://openalex.org/W2539939190Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1090/tran/7634Digital Object Identifier
- Title
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The geometry of stable minimal surfaces in metric Lie groupsWork title
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articleOpenAlex work type
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enPrimary language
- Publication year
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2018Year of publication
- Publication date
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2018-06-20Full publication date if available
- Authors
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William H. Meeks, Pablo Mira, Joaquín PérezList of authors in order
- Landing page
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https://doi.org/10.1090/tran/7634Publisher landing page
- PDF URL
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https://www.ams.org/tran/2019-372-02/S0002-9947-2019-07634-1/S0002-9947-2019-07634-1.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
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bronzeOpen access status per OpenAlex
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https://www.ams.org/tran/2019-372-02/S0002-9947-2019-07634-1/S0002-9947-2019-07634-1.pdfDirect OA link when available
- Concepts
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Mathematics, Geodesic, Semidirect product, Minimal surface, Lie group, Boundary (topology), Invariant (physics), Geometry, Pure mathematics, Context (archaeology), Mathematical analysis, Combinatorics, Group (periodic table), Mathematical physics, Paleontology, Chemistry, Biology, Organic chemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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5Total citation count in OpenAlex
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2025: 1, 2023: 1, 2022: 1, 2020: 1, 2019: 1Per-year citation counts (last 5 years)
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31Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W2073411244, https://openalex.org/W2103392187, https://openalex.org/W1533120858, https://openalex.org/W1565927722, https://openalex.org/W2037972078, https://openalex.org/W2039759412, https://openalex.org/W2049748003, https://openalex.org/W2105099706, https://openalex.org/W2963041199, https://openalex.org/W2156746708, https://openalex.org/W2562682952, https://openalex.org/W3195237645, https://openalex.org/W2113578733, https://openalex.org/W3104962745, https://openalex.org/W2079088760, https://openalex.org/W2475464023, https://openalex.org/W1998611699, https://openalex.org/W1619464273, https://openalex.org/W1598622792, https://openalex.org/W2964344420, https://openalex.org/W2568145020, https://openalex.org/W1998222042, https://openalex.org/W2005899545, https://openalex.org/W1996000545, https://openalex.org/W2325505781, https://openalex.org/W2044087461, https://openalex.org/W2963819634, https://openalex.org/W3105832498, https://openalex.org/W3099356885, https://openalex.org/W3105977352, https://openalex.org/W2326065890 |
| referenced_works_count | 31 |
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