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Tytuł artykułu

Invertible Carnot Groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.
Wydawca
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2013-12-12
zaakceptowano
2014-08-11
online
2014-09-19
Twórcy
  • University of Cincinnati Blue Ash College, 9555 Plainfield Road, Cincinnati, Ohio 45236, david.freeman@uc.edu
Bibliografia
  • [1] Jürgen Berndt, Franco Tricerri, and Lieven Vanhecke. Generalized Heisenberg groups and Damek-Ricci harmonic spaces, volume 1598 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1995.
  • [2] Mario Bonk and Bruce Kleiner. Quasisymmetric parametrizations of two-dimensional metric spheres. Invent. Math., 150(1):127-183, 2002.
  • [3] Mario Bonk and Bruce Kleiner. Rigidity for quasi-Möbius group actions. J. Diferential Geom., 61(1):81-106, 2002.
  • [4] Mario Bonk and Bruce Kleiner. Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary. Geom. Topol., 9:219-246 (electronic), 2005.
  • [5] Stephen M. Buckley, David A. Herron, and Xiangdong Xie. Metric space inversions, quasihyperbolic distance, and uniform spaces. Indiana Univ. Math. J., 57(2):837-890, 2008.
  • [6] Sergei Buyalo and Viktor Schroeder. Möbius characterization of the boundary at infinity of rank one symmetric spaces. Geom. Dedicata, pages 1-45, 2013.
  • [7] Luca Capogna and Michael Cowling. Conformality and Q-harmonicity in Carnot groups. DukeMath. J., 135(3):455-479, 2006.
  • [8] Michael Cowling, Anthony H. Dooley, Adam Korányi, and Fulvio Ricci. H-type groups and Iwasawa decompositions. Adv. Math., 87(1):1-41, 1991.
  • [9] Michael Cowling, Anthony H. Dooley, Adam Korányi, and Fulvio Ricci. An approach to symmetric spaces of rank one via groups of Heisenberg type. J. Geom. Anal., 8(2):199-237, 1998.[Crossref]
  • [10] Michael Cowling and Alessandro Ottazzi. Conformal maps of Carnot groups. preprint, page arXiv:1312.6423, 2013.
  • [11] David M. Freeman. Inversion invariant bilipschitz homogeneity. Michigan Math. J., 61(2):415-430, 2012.
  • [12] David M. Freeman. Transitive bi-Lipschitz group actions and bi-Lipschitz parameterizations. Indiana Univ. Math. J., 62(1):311-331, 2013.[WoS]
  • [13] Juha Heinonen and Pekka Koskela. Quasiconformalmaps in metric spaceswith controlled geometry. ActaMath., 181(1):1-61, 1998.
  • [14] Kyle Edward Kinneberg. Rigidity for quasi-Möbius actions on fractal metric spaces. arXiv:1308:0639, 2013.
  • [15] Linus Kramer. Two-transitive Lie groups. J. Reine Angew. Math., 563:83-113, 2003.
  • [16] Enrico Le Donne. Geodesic manifolds with a transitive subset of smooth biLipschitz maps. Groups Geom. Dyn., 5(3):567-602, 2011.
  • [17] Enrico Le Donne. Metric spaces with unique tangents. Ann. Acad. Sci. Fenn. Math., 36(2):683-694, 2011.[Crossref]
  • [18] Jussi Väisälä. Quasi-Möbius maps. J. Analyse Math., 44:218-234, 1984/85.
  • [19] Xiangdong Xie. Quasiconformal maps on model Filiform groups. preprint, page arXiv:1308.3027, 2013.
  • [20] Xiangdong Xie. Quasiconformal maps on non-rigid Carnot groups. preprint, page arXiv:1308.3031, 2013.
  • [21] Xiangdong Xie. Rigidity of quasiconformal maps on Carnot groups. preprint, page arXiv:1308.3028, 2013.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_agms-2014-0009
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