Journal ArticleDOI
Topology of three dimensional manifolds and the embedding problems in minimal surface theory
William H. Meeks,Shing-Tung Yau +1 more
Reads0
Chats0
About:
This article is published in Annals of Mathematics.The article was published on 1980-11-01. It has received 243 citations till now. The article focuses on the topics: Extension topology & Initial topology.read more
Citations
More filters
Journal ArticleDOI
Three dimensional manifolds, Kleinian groups and hyperbolic geometry
TL;DR: In the case of negative Euler characteristic (genus greater than 1) such a metric gives a hyperbolic structure: any small neighborhood in a surface is isometric to a neighborhood in the hyper-bolic plane, and the surface itself is the quotient of the hyperbola by a discrete group of motions as discussed by the authors.
Journal ArticleDOI
The inverse mean curvature flow and the Riemannian Penrose Inequality
Gerhard Huisken,Tom Ilmanen +1 more
TL;DR: In this article, a theory of weak solutions of the inverse mean curvature flow was developed and employed to prove the Riemannian Penrose inequality for each connected component of a 3-manifold of nonnegative scalar curvature.
Journal ArticleDOI
Varieties of group representations and splittings of 3-manifolds
Marc Culler,Peter B. Shalen +1 more
Journal ArticleDOI
Another Report on Harmonic Maps
James Eells,Luc Lemaire +1 more
TL;DR: In this paper, it was shown that a map (f>:{M,g)-+(N,h) between Riemannian manifolds which is continuous and of class L\\ is harmonic if and only if it is a critical point of the energy functional.
Journal ArticleDOI
Notes on Perelman's papers
Bruce Kleiner,John Lott +1 more
TL;DR: In this paper, the Ricci flow with surgery with surgery was shown to die in a finite time, which is the case for the Poincar´ e Conjecture.
References
More filters
Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Book
Geometric Measure Theory
TL;DR: In this article, Grassmann algebras of a vectorspace have been studied in the context of the calculus of variations, and a glossary of some standard notations has been provided.
Book
Introduction to Piecewise-Linear Topology
Colin Rourke,Brian Sanderson +1 more
TL;DR: In this article, the Poincare Conjecture and the h-Cobordism Theorem are used to prove the existence of a double-cobordist.
Book
Geometry of Manifolds
TL;DR: Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete RiemANNian manifoldolds Riemmannian curvature Immersions and the second fundamental form Second variation of arc length Theorems on differential equations Bibliography Subject index as mentioned in this paper
Related Papers (5)
Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
Richard Schoen,Shing-Tung Yau +1 more
On the proof of the positive mass conjecture in general relativity
Richard Schoen,Shing-Tung Yau +1 more