Minimal surfaces in Euclidean spaces by way of complex analysis

DOI10.4171/8ecm/08arXiv2108.13347OpenAlexW4384298706MaRDI QIDQ6086347

Franc Forstnerič

Publication date: 10 November 2023

Published in: European Congress of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.13347

zbMATH Keywords

minimal surfaceCalabi-Yau problemconformal harmonic map

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Calabi-Yau theory (complex-analytic aspects) (32Q25) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Conformal structures on manifolds (53C18)

Cites Work

• Embedded minimal surfaces in \(\mathbb R^n\)
• Every bordered Riemann surface is a complete proper curve in a ball
• Minimal surfaces in \(\mathbb{R}^3\) properly projecting into \(\mathbb{R}^2\)
• On subharmonic functions and differential geometry in the large
• Holomorphe Funktionen mit Werten in komplexen Lieschen Gruppen
• Oka manifolds
• The Calabi-Yau problem, null curves, and Bryant surfaces
• A complete complex hypersurface in the ball of \(\mathbb{C}^N\)
• The topology of complete minimal surfaces of finite total Gaussian curvature
• A complete minimal surface in \(R^ 3\) between two parallel planes
• The classification of complete minimal surfaces in \(R^ 3\) with total curvature greater than -8pi
• The existence of embedded minimal surfaces and the problem of uniqueness
• The classical Plateau problem and the topology of three-dimensional manifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's lemma
• Curvatures of complex submanifolds of \(C^n\)
• Interpolation by conformal minimal surfaces and directed holomorphic curves
• Complete minimal surfaces densely lying in arbitrary domains of \(\mathbb{R}^n\)
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected
• The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds
• The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends
• The embedded Calabi-Yau conjecture for finite genus
• Holomorphic Legendrian curves in \(\mathbb{CP}^3\) and superminimal surfaces in \(\mathbb{S}^4\)
• Algebraic approximation and the Mittag-Leffler theorem for minimal surfaces
• Complete complex hypersurfaces in the ball come in foliations
• A foliation of the ball by complete holomorphic discs
• Null curves and directed immersions of open Riemann surfaces
• Every meromorphic function is the Gauss map of a conformal minimal surface
• Fixed points, Koebe uniformization and circle packings
• The uniqueness of the helicoid
• A construction of complete complex hypersurfaces in the ball with control on the topology
• The Calabi-Yau conjectures for embedded surfaces
• Complete minimal surfaces in Euclidean \(n\)-spaces
• Immersion of open Riemann surfaces
• Approximation von holomorphen Schnittflächen in Faserbündeln mit homogener Faser
• The parametric \(h\)-principle for minimal surfaces in \(\mathbb{R}^n\) and null curves in \(\mathbb{C}^n\)
• Entwicklung analytischer Funktionen auf Riemannschen Flächen
• The classical theory of minimal surfaces
• Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan
• Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves: Figure. 5.1.
• Seminar on Differential Geometry. (AM-102)
• Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
• New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in ℝⁿ
• Darboux Charts Around Holomorphic Legendrian Curves and Applications
• Stein Manifolds and Holomorphic Mappings
• Holomorphic Legendrian curves
• Shapes of embedded minimal surfaces
• Absolute neighbourhood retracts and spaces of holomorphic maps from Stein manifolds to Oka manifolds
• The Riemann minimal examples
• The geometry of $G$-structures
• Bounded Holomorphic Functions on Finite Riemann Surfaces
• Minimal Surfaces from a Complex Analytic Viewpoint
• Review of geometry and analysis
• Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Minimal surfaces in Euclidean spaces by way of complex analysis