The topological uniqueness of complete one-ended minimal surfaces and Heegaard surfaces in ℝ³

DOI10.1090/S0894-0347-97-00215-4zbMath0886.57015OpenAlexW1490743809MaRDI QIDQ4372710

William Hamilton III Meeks, Charles D. Frohman

Publication date: 16 December 1997

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0894-0347-97-00215-4

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items

The global theory of doubly periodic minimal surfaces, On non-compact Heegaard splittings, An unknotting result for complete minimal surfaces in \(\mathbb{R}^ 3\), The topology of complete one-ended minimal surfaces and Heegaard surfaces in 𝑅³, The strong halfspace theorem for minimal surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The topological uniqueness of triply periodic minimal surfaces in \(R^ 3\)
• 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
• Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
• On complete minimal surfaces with finite Morse index in three manifolds
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• Minimal surfaces and Heegaard splittings of the three-torus
• Reducing Heegaard splittings
• Unstable minimal surfaces and Heegaard splittings
• The topological uniqueness of minimal surfaces in three dimensional euclidean space
• The existence of embedded minimal surfaces and the problem of uniqueness
• Least area incompressible surfaces in 3-manifolds
• 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
• The topological uniqueness of complete minimal surfaces of finite topological type
• On the Heegaard splitting of the torus \(T^ 3\)
• Heegaard-Zerlegungen der 3-Sphäre
• Boundary behavior of minimal surfaces
• The unknottedness of minimal embeddings
• Adding handles to the helicoid
• Scindements de Heegaard des espaces lenticulaires
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Stable complete minimal surfaces in 𝑅³ are planes
• Three-Dimensional Manifolds and Their Heegaard Diagrams
• Boundary regularity and embedded solutions for the oriented Plateau problem