Gromov boundary information

mathematics, the Gromov boundary of a δ-hyperbolic space (especially a hyperbolic group) is an abstract concept generalizing the boundary sphere of hyperbolic...

of a group; hyperbolicity of a group; the homeomorphism type of the Gromov boundary of a hyperbolic group; asymptotic cones of finitely generated groups...

nonnegative real number δ) between points. The definition, introduced by Mikhael Gromov, generalizes the metric properties of classical hyperbolic geometry and...

non-elementary Gromov-hyperbolic groups. This simple folklore proof uses dynamical properties of the action of hyperbolic elements on the Gromov boundary of a Gromov-hyperbolic...

first moment be finite) the Poisson boundary is always equal to the Gromov boundary. For example, the Poisson boundary of a free group is the space of ends...

mathematics, the Gromov product is a concept in the theory of metric spaces named after the mathematician Mikhail Gromov. The Gromov product can also...

group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word metric...

explicit geometric realisation of a compactification defined by Gromov—by adding an "ideal boundary"—for the more general class of proper metric spaces X, those...

relation. The action of a finitely-generated hyperbolic group on its Gromov boundary is hyperfinite. Any countable Borel equivalence relation can be restricted...

polyhedra, as initially conceived by Charles Loewner and developed by Mikhail Gromov, Michael Freedman, Peter Sarnak, Mikhail Katz, Larry Guth, and others, in...

physics, Alexandrov spaces arising as Gromov–Hausdorff limits of sequences of Riemannian manifolds, and boundaries and asymptotic cones in geometric group...

In differential geometry, Mikhail Gromov's filling area conjecture asserts that the hemisphere has minimum area among the orientable surfaces that fill...

theory is the number of pseudo holomorphic maps f : M → X in the sense of Gromov (they are ordinary holomorphic maps if X is a Kähler manifold). If this...

spaces of negative curvature. Hyperbolic space serves as the prototype of a Gromov hyperbolic space, which is a far-reaching notion including differential-geometric...

manifold with curvature zero. In 1970's and early 80's, Thierry Aubin, Misha Gromov, Yuri Burago, and Viktor Zalgaller conjectured that the Euclidean isoperimetric...

Witten with different techniques. Schoen and Yau, and independently Mikhael Gromov and Blaine Lawson, developed a number of fundamental results on the topology...

dimension introduced in 1999 by Mikhail Gromov. In related work he introduced and studied the small boundary property and stated fundamental conjectures...

two problems of Loewner, J. London Math. Soc. 27 (1952) 141–144. Mikhael Gromov. Filling Riemannian manifolds. J. Differential Geom. 18 (1983), no. 1, 1-147...

Archived from the original on 20 March 2017. Retrieved 1 February 2012. Gromov, Mikhael (1983). "Filling Riemannian manifolds". Journal of Differential...

Lisa W. (31 May 2009). "In N.Y.U.'s Tally of Abel Prizes for Mathematics, Gromov Makes Three". The New York Times. Archived from the original on 2 April...

most six times its filling radius, see (Gromov, 1983). The inequality is optimal in the sense that the boundary case of equality is attained by the real...

enumerates certain pseudoholomorphic curves and is now known as Taubes's Gromov invariant. This fact improved mathematicians' understanding of the topology...

its Bowditch boundary ∂ G {\displaystyle \partial G} is a convergence group action. Let X {\displaystyle X} be a proper geodesic Gromov-hyperbolic metric...