Shrinkwrapping and the taming of hyperbolic 3-manifolds

DOI10.1090/S0894-0347-05-00513-8zbMath1090.57010arXivmath/0407161OpenAlexW2149889673MaRDI QIDQ3376941

David Gabai, Danny Calegari

Publication date: 27 March 2006

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

Full work available at URL: https://arxiv.org/abs/math/0407161

zbMATH Keywords

tameclassificationminimal surfaceconjecturelaminationtamenessendgeometrically finiteCAT(-1)BersThurstonend reductionendingAhlforsBonahonBrinCanaryend movablegeometrically infiniteMardensimply degenerateThickstun

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) General geometric structures on low-dimensional manifolds (57M50) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• The classification of Kleinian surface groups. II: The Ending lamination conjecture
• Existence of ruled wrappings in hyperbolic 3-manifolds
• Coincidence set of minimal surfaces for the thin obstacle
• Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• Open, irreducible 3-manifolds which are end 1-movable
• Bouts des variétés hyperboliques de dimension 3. (Ends of hyperbolic 3-dimensional manifolds)
• Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
• The smoothness of the solution of the boundary obstacle problem
• 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
• Two dimensional variational problems with thin obstacles
• Homeomorphisms of sufficiently large \(P^2\)-irreducible 3-manifolds
• Homotopy equivalences of 3-manifolds with boundaries
• Kneser-Haken finiteness for bounded 3-manifolds, locally free groups, and cyclic covers
• Homotopy hyperbolic 3-manifolds are hyperbolic
• A note on the tameness of hyperbolic 3-manifolds
• The geometry of finitely generated Kleinian groups
• Non-compact 3-manifolds and the missing-boundary problem
• Tameness on the boundary and Ahlfors' measure conjecture
• On the density of geometrically finite Kleinian groups.
• On limits of tame hyperbolic 3-manifolds
• A covering theorem for hyperbolic 3-manifolds and its applications
• End reductions, fundamental groups, and covering spaces of irreducible open 3-manifolds
• Algebraic limits of geometrically finite manifolds are tame
• On irreducible 3-manifolds which are sufficiently large
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Variational problems with inequalities as boundary conditions or how to fashion a cheap hat for Giacometti's brother
• On the coincidence set in variational inequalities
• Vol3 and other exceptional hyperbolic 3-manifolds
• Uniqueness of Cores of Non-Compact 3-Manifolds
• Local behavior of solutions of general linear elliptic equations
• A Lower Bound for the Volume of Hyperbolic 3-Manifolds
• 3-manifolds which are end 1-movable
• The Existence of Least Area Surfaces in 3-Manifolds
• On Properly Embedding Planes in Arbitrary 3-Manifolds
• COMPACT SUBMANIFOLDS OF 3-MANIFOLDS WITH BOUNDARY
• Further regularity for the signorini problem
• Ends of Hyperbolic 3-Manifolds
• ON THE FOX-ARTIN SPHERE AND SURFACES IN NONCOMPACT 3-MANIFOLDS
• Tameness persists in weakly type-preserving strong limits
• FUNDAMENTAL POLYHEDRONS AND LIMIT POINT SETS OF KLEINIAN GROUPS
• Finitely Generated Kleinian Groups
• Shapes of embedded minimal surfaces
• Exceptional Regions and Associated Exceptional Hyperbolic 3-Manifolds
• Compact Submanifolds of 3-Manifolds
• On the geometric and topological rigidity of hyperbolic 3-manifolds
• Kleinian groups which are limits of geometrically finite groups
• Foliations and the topology of 3-manifolds
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Riemannian geometry and geometric analysis