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

Mikhael Leonidovich Gromov (also Mikhail Gromov, Michael Gromov or Misha Gromov; Russian: Михаи́л Леони́дович Гро́мов; born 23 December 1943) is a Russian-French...

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...

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

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

Poisson boundary is always equal to the Gromov boundary when equipped with the hitting probability measure. For example, the Poisson boundary of a free...

examples, see for instance hyperbolic boundary, Gromov boundary, visual boundary, Tits boundary, Thurston boundary. See also projective space and compactification...

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...

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...

_{1}({\mathcal {H}}(K))} is a Gromov hyperbolic group. The hyperbolizing cell in this procedure is a real hyperbolic manifold with boundary and corners constructed...

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

G\to \mathbb {S} ^{2}} , where ∂ G {\displaystyle \partial G} is the Gromov boundary of G, and where the image of j is the limit set of G in S 2 {\displaystyle...

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

February 23 – Erich Kästner, German writer (d. 1974) February 24 – Mikhail Gromov, Soviet aviator (d. 1985) February 26 – Alec Campbell, Australian WWI soldier...

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

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...

2000. Callahan, Hildebrand & Weeks 1999. Gromov & Thurston 1987. Aschenbrenner, Friedl & Wilton 2015. Gromov 1981. Aschenbrenner, Matthias; Friedl, Stefan;...

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

d(x,y)+d(y,z).} Metametrics appear in the study of Gromov hyperbolic metric spaces and their boundaries. The visual metametric on such a space satisfies...

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

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...

difference in internal metrics between the hemisphere and the disk led Mikhael Gromov to pose his filling area conjecture, according to which the unit hemisphere...

is the pen name of Ukrainian science fiction and fantasy writers Dmitry Gromov and Oleg Ladyzhensky. Both authors reside in Kharkiv, Ukraine, and write...

group theory. The main purpose in their study is to extend the theory of Gromov-hyperbolic groups to groups G {\textstyle G} that may be regarded as hyperbolic...

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

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

In mathematics, the 2π theorem of Gromov and Thurston states a sufficient condition for Dehn filling on a cusped hyperbolic 3-manifold to result in a negatively...

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...

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...