Complete minimal surfaces densely lying in arbitrary domains of \(\mathbb{R}^n\)
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Publication:1676777
DOI10.2140/gt.2018.22.571zbMath1378.53070arXiv1611.05029OpenAlexW2963292812MaRDI QIDQ1676777
Antonio Alarcón, Ildefonso Castro-Infantes
Publication date: 10 November 2017
Published in: Geometry \& Topology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1611.05029
Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)
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Minimal surfaces in Euclidean spaces by way of complex analysis ⋮ NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY ⋮ Interpolation by complete minimal surfaces whose Gauss map misses two points ⋮ The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones ⋮ Holomorphic Legendrian curves in \(\mathbb{CP}^3\) and superminimal surfaces in \(\mathbb{S}^4\) ⋮ Complete densely embedded complex lines in ℂ²
Cites Work
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- Embedded minimal surfaces in \(\mathbb R^n\)
- Proper holomorphic embeddings of Riemann surfaces with arbitrary topology into \({\mathbb C^2}\)
- Every bordered Riemann surface is a complete proper curve in a ball
- Oka manifolds: from Oka to Stein and back
- Minimal surfaces in \(\mathbb{R}^3\) properly projecting into \(\mathbb{R}^2\)
- Exotic minimal surfaces
- Survey of Oka theory
- Subalgebras of functions on a Riemann surface
- The Calabi-Yau problem, null curves, and Bryant surfaces
- Holomorphic curves in complex spaces
- Bordered Riemann surfaces in \(\mathbb C^2\)
- Surjective holomorphic maps onto Oka manifolds
- Complete minimal surfaces and harmonic functions
- Non-degenerate maps and sets
- Null curves and directed immersions of open Riemann surfaces
- Approximation theory for nonorientable minimal surfaces and applications
- Complex geometry and dynamics. The Abel symposium 2013, Trondheim, Norway, July 2--5, 2013
- Holomorphic discs with dense images
- Dense solutions to the Cauchy problem for minimal surfaces
- The Poletsky-Rosay theorem on singular complex spaces
- Flexibility Properties in Complex Analysis and Affine Algebraic Geometry
- Stein Manifolds and Holomorphic Mappings
- Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves: Figure. 5.1.
- A wild minimal plane in ℝ³
- Holomorphic Legendrian curves
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