In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale...

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed...

(bijective) isometry between them. In this case, the two metric spaces are essentially identical. They are called quasi-isometric if there is a quasi-isometry between...

invariant of G. Modern geometric group theory is in large part the study of quasi-isometry invariants. Length function Longest element of a Coxeter group J. W...

require invariance under quasi-isometry. This is true of hyperbolicity. If a geodesic metric space Y {\displaystyle Y} is quasi-isometric to a δ {\displaystyle...

a quasi-isometry is not assumed to be continuous. For example, any map between compact metric spaces is a quasi isometry. If there exists a quasi-isometry...

R^{n+1}(X)} . The quasi-isometry properties of the history graph can be studied using subdivision rules. For instance, the history graph is quasi-isometric to...

Isometry group Quasi-isometry Dade isometry Euclidean isometry Euclidean plane isometry Itō isometry Isometric (disambiguation) Isometries in physics This...

their word metric up to quasi-isometry. This program involves: The study of properties that are invariant under quasi-isometry. Examples of such properties...

necessarily be quasi-equivalent; that quasi-isometries are closed under composition which up to quasi-equivalence depends only the quasi-equivalence classes;...

mathematical ideas into the drawings." The quasi-isometry classification of rank one lattices: Any quasi-isometry of a hyperbolic lattice is equivalent to...

measure the difference between two shapes. In advanced mathematics, quasi-isometry can be used as a criterion to state that two shapes are approximately...

{\displaystyle X} , is quasi-isometric to X {\displaystyle X} . This result goes back, in different form, before the notion of quasi-isometry was formally introduced...

Quasi-equivalence could refer to Weak equivalence (homotopy theory) Quasi-isometry Quasi-isomorphism The Caspar-Klug theory of viral capsids. This disambiguation...

latter depends on both the original δ {\displaystyle \delta } and on the quasi-isometry, thus it does not make sense to speak of G {\displaystyle G} being δ...

reducing distance between all points Dini continuity Modulus of continuity Quasi-isometry Johnson–Lindenstrauss lemma – For any integer n≥0, any finite subset...

Fenchel-Nielsen coordinates are bounded by a large enough constant. It is a quasi-isometry when Teichmüller space is endowed with the Weil-Petersson metric, which...

Gromov boundary is a quasi-isometry invariant; that is, if two Gromov-hyperbolic metric spaces are quasi-isometric, then the quasi-isometry between them induces...

invariants of infinite groups in the context of geometric group theory, as a quasi-isometry invariant of finitely generated groups. As shown by Guoliang Yu, finitely...

research area is geometric group theory; in particular, she studies quasi-isometry invariants of groups. Dani received a B.Sc. degree in mathematics from...

relatively compact. Bornology – Mathematical generalization of boundedness Quasi-isometry – Function between two metric spaces that only respects their large-scale...

507–544. doi:10.1002/cpa.3160330404. MR 0575736. Yeung, Sai-Kee (2005). "Quasi-isometry of metrics on Teichmüller spaces". Int. Math. Res. Not. 2005 (4): 239–255...

cancellation presentations to prove that there exist continuumly many quasi-isometry types of two-generator groups. Thomas and Velickovic used small cancellation...

precisely, their topological types and bi-Lipschitz types) provide quasi-isometry invariants of metric spaces in general and of finitely generated groups...

classification of relatively hyperbolic groups up to quasi-isometry; the fact that a group with a quasi-isometric embedding in a relatively hyperbolic metric...

relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The Dehn function of a finitely...

foundational examples of isometric group actions. Other major topics include quasi-isometries, Gromov-hyperbolic groups and their generalizations (relatively and...

co-Hopfian group need not be co-Hopfian, and being co-Hopfian is not a quasi-isometry invariant for finitely generated groups. Baumslag–Solitar groups B S...

(1989), no. 1, 1–60. Bruce Kleiner and Bernhard Leeb. Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings. Inst. Hautes Études Sci...

are, by definition, discrete subgroups of the isometry group of hyperbolic 3-space. These include quasi-Fuchsian groups. A Kleinian group that preserves...