The Michigan Mathematical Journal

Quasi-conformal maps on model Filiform groups

Xiangdong Xie

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Michigan Math. J., Volume 64, Issue 1 (2015), 169-202.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1427203290

Digital Object Identifier
doi:10.1307/mmj/1427203290

Mathematical Reviews number (MathSciNet)
MR3326585

Zentralblatt MATH identifier
1339.22006

Subjects
Primary: 22E25: Nilpotent and solvable Lie groups 30L10: Quasiconformal mappings in metric spaces
Secondary: 53C17: Sub-Riemannian geometry

Citation

Xie, Xiangdong. Quasi-conformal maps on model Filiform groups. Michigan Math. J. 64 (2015), no. 1, 169--202. doi:10.1307/mmj/1427203290. https://projecteuclid.org/euclid.mmj/1427203290


Export citation

References

  • Z. Balogh, Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group, J. Anal. Math. 83 (2001), 289–312.
  • Z. Balogh, P. Koskela, and S. Rogovin, Absolute continuity of quasiconformal mappings on curves, Geom. Funct. Anal. 17 (2007), no. 3, 645–664.
  • A. Bellaiche and J. J. Risler, Sub-Riemannian geometry, Progr. Math., 144, Birkhäuser Verlag, Basel, 1996.
  • L. Capogna and M. Cowling, Conformality and Q-harmonicity in Carnot groups, Duke Math. J. 135 (2006), no. 3, 455–479.
  • L. Corwin and F. Greenleaf, Representations of nilpotent Lie groups and their applications, Part I. Basic theory and examples, Cambridge Stud. Adv. Math., 18, Cambridge University Press, Cambridge, 1990.
  • E. Heintze, On homogeneous manifolds of negative curvature, Math. Ann. 211 (1974), 23–34.
  • J. Heinonen and P. Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1–61.
  • A. Ottazzi, A sufficient condition for nonrigidity of Carnot groups, Math. Z. 259 (2008), no. 3, 617–629.
  • A. Ottazzi and B. Warhurst, Contact and 1-quasiconformal maps on Carnot groups, J. Lie Theory 21 (2011), no. 4, 787–811.
  • P. Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés, Ergodic Theory Dynam. Systems 3 (1983), no. 3, 415–445.
  • –-, Metriques de Carnot-Caratheodory et quasiisometries des espaces symetriques de rang un, Ann. of Math. (2) 129 (1989), no. 1, 1–60.
  • H. M. Reimann and F. Ricci, The complexified Heisenberg group, Proceedings on analysis and geometry (Russian) (Novosibirsk Akademgorodok, 1999), pp. 465–480, Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000.
  • N. Shanmugalingam and X. Xie, A rigidity property of some negatively curved solvable Lie groups, Comment. Math. Helv. 87 (2012), no. 4, 805–823.
  • J. Tyson, Metric and geometric quasiconformality in Ahlfors regular Loewner spaces, Conform. Geom. Dyn. 5 (2001), 21–73.
  • J. Väisälä, The free quasiworld. Freely quasiconformal and related maps in Banach spaces, Quasiconformal geometry and dynamics (Lublin, 1996), Banach Center Publ., 48, pp. 55–118, Polish Acad. Sci., Warsaw, 1996.
  • B. Warhurst, Contact and quasiconformal mappings on real model filiform groups, Bull. Aust. Math. Soc. 68 (2003), no. 2, 329–343.
  • X. Xie, Some examples of quasiisometries of nilpotent Lie groups, J. Reine Angew. Math. (to appear).
  • –-, Rigidity of quasiconformal maps on Carnot groups, $\langle$\surlhttp://front.math. ucdavis.edu/1308.3028$\rangle$.
  • –-, Quasisymmetric maps on reducible Carnot groups, Pacific J. Math. 265 (2013), no. 1, 113–122.
  • –-, Quasiconformal maps on non-rigid Carnot groups, $\langle$\surlhttp://front.math. ucdavis.edu/1308.3031$\rangle$. \printaddresses