In Riemannian geometry, a collapsing or collapsed manifold is an n-dimensional manifold M that admits a sequence of Riemannian metrics gi, such that as...

diameter going to zero, so the almost-flat manifold is a special case of a collapsing manifold, which is collapsing along all directions. According to the...

concept Collapsing manifold Collapse, the action of collapsing or telescoping objects Collapsing user interface elements Accordion (GUI) -- collapsing list...

where g is a continuous function from B0 into A0. Perelman’s collapsing theorem for 3-manifolds, the capstone of his proof of Thurston's geometrization conjecture...

Perelman's collapsing theorem for 3-manifolds. J. Geom. Anal. 21 (2011), no. 4, 807–869. Kleiner, Bruce; Lott, John. Locally collapsed 3-manifolds. Astérisque...

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature...

symbol Coarse geometry Collapsing manifold Complete manifold According to the Riemannian Hopf-Rinow theorem, a Riemannian manifold is complete as a metric...

manifolds while keeping their curvature bounded, II, with Mikhail Gromov. Journal of Differential Geometry. 31, 4. 1990. 269–298. Collapsing manifold...

"Locally collapsed 3-manifolds". Astérisque. 365 (7–99). Cao, Jianguo; Ge, Jian (2011). "A simple proof of Perelman's collapsing theorem for 3-manifolds". J...

Memorial Lectures. Cartan–Hadamard conjecture Cartan–Hadamard theorem Collapsing manifold Lévy–Gromov inequality Taubes's Gromov invariant Mostow rigidity...

gave a talk entitled, Collapsing Riemannian Manifolds and its Applications. Fukaya, Kenji (1987). "Collapsing Riemannian Manifolds and Eigenvalues of Laplace-Operators"...

small diameter or large curvature. They show that the 3-sphere is a collapsing manifold: it admits a sequence of Riemannian metrics with uniformly bounded...

subject. Manifold Destiny Matveev, Sergei (2007). "1.3.4 Zeeman's Collapsing Conjecture". Algorithmic Topology and Classification of 3-Manifolds. Algorithms...

Manifold: Time is a 1999 science fiction novel by Stephen Baxter. It is the first of Baxter's Manifold Trilogy (the others being Manifold: Space and Manifold:...

These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere...

aspect of a smooth manifold's topology. This diffeomorphism invariant was introduced by Mikhael Gromov. Given a smooth Riemannian manifold (M, g), one may...

air directly into the atmosphere. A vacuum hose connected to the intake manifold downstream of the throttle provides a reference pressure for the blowoff...

of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in anti-de Sitter space. Wormholes are consistent with...

manifolds. Its effect is to decompose a given manifold into two pieces. There is an inverse operation, the symplectic sum, that glues two manifolds together...

theorems embed any abstract manifold in some Euclidean space. The Nash embedding theorem embeds an abstract Riemannian manifold isometrically in a Euclidean...

It assumes that the shape of the internal manifold is a Calabi–Yau manifold or generalized Calabi–Yau manifold which is equipped with non-zero values of...

renormalized to preserve volume. (Under the unrenormalized Ricci flow, the manifold collapses to a point in finite time.) However, this doesn't prove the full geometrization...

(homotopy equivalent to a point), but not collapsible. Any n-dimensional PL manifold that is collapsible is in fact piecewise-linearly isomorphic to an n-ball...

temperature is no longer high enough to prevent it from collapsing under its own weight. The collapse may be stopped by the degeneracy pressure of the star's...

geometrical theory of gravitation are tensor fields defined on a Lorentzian manifold representing spacetime. This article is a general description of the mathematics...

together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping. In complex analysis, the basic model can...

four basic types of breaking water waves. They are spilling, plunging, collapsing, and surging. When the ocean floor has a gradual slope, the wave will...

time where the curvature becomes infinite, or spacetime stops being a manifold. Singularities can be found in all the black-hole spacetimes, the Schwarzschild...

In mathematics, a nilmanifold is a differentiable manifold which has a transitive nilpotent group of diffeomorphisms acting on it. As such, a nilmanifold...

center manifold. In other words, the 4-dimensional system collapses onto a 2-dimensional plane. Any solution starting off the center manifold will decay...