Some uniqueness and nonexistence theorems for embedded minimal surfaces

DOI10.1007/BF01444900zbMath0789.53004OpenAlexW2053023959MaRDI QIDQ1318022

Joaquín Pérez, Antonio Ros

Publication date: 22 June 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165055

zbMATH Keywords

finite total curvatureannulusperiodic minimal surfacesminimal tori

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (15)

Geodesics in minimal surfaces ⋮ Complete embedded minimal surfaces of finite total curvature with planar ends of smallest possible order ⋮ Embedded minimal surfaces: Forces, topology and symmetries ⋮ Symmetry of embedded genus 1 helicoids ⋮ On singly-periodic minimal surfaces with planar ends ⋮ Symmetry and rigidity of minimal surfaces with Plateau-like singularities ⋮ A rigidity theorem for Riemann's minimal surfaces ⋮ On uniqueness of Riemann’s examples ⋮ Minimal surfaces in ${\mathbb{R}}^{4}$ foliated by conic sections and parabolic rotations of holomorphic null curves in ${\mathbb{C}}^{4}$ ⋮ The embedded Calabi-Yau conjecture for finite genus ⋮ Remarks on minimal annuli in a slab ⋮ On harmonic quasiconformal immersions of surfaces in $\mathbb {R}^3$ ⋮ A CHARACTERIZATION OF THE CATENOID AND HELICOID ⋮ The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends ⋮ Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

Cites Work

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• The maximum principle at infinity for minimal surfaces in flat three manifolds
• The strong halfspace theorem for minimal surfaces
• The structure of singly-periodic minimal surfaces
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• A complete embedded minimal surface in \({\mathbb{R}}^ 3\) with genus one and three ends
• Un théorème d'unicité de l'hélicoïde. (A uniqueness theorem for the helicoid)
• Embedded minimal surfaces derived from Scherk's examples
• A maximum principle at infinity for minimal surfaces and applications
• Embedded minimal surfaces with an infinite number of ends
• The global theory of doubly periodic minimal surfaces
• Embedded minimal annuli in \(\mathbb{R}^ 3\) bounded by a pair of straight lines
• On the minimal surfaces of Riemann
• The geometry of periodic minimal surfaces
• On embedded complete minimal surfaces of genus zero
• Example of a complete minimal immersion in IR3 of genus one and three-embedded ends

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