Topology of three dimensional manifolds and the embedding problems in minimal surface theory. (English) Zbl 0458.57007

Meeks, William H. III; Yau, Shing-Tung

Ann. Math. (2) 112, 441-484 (1980).

MSC:

57M35	Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)
57N10	Topology of general \(3\)-manifolds (MSC2010)
57N35	Embeddings and immersions in topological manifolds
58E12	Variational problems concerning minimal surfaces (problems in two independent variables)
49Q05	Minimal surfaces and optimization
53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)

Keywords:

loop theorem; sphere theorem; finite group action; 3 dimensional Riemannian manifold; harmonic mapping of least area; number of free homotopy classes of mappings having Dirichlet integral not exceeding a fixed number; orientation preserving diffeomorphism of finite order of 3- space