Pekka Tukia

Pekka Tukia is a Finnish mathematician[1] who does research on Kleinian groups and their geometric properties (such as limit sets).

Tukia received his PhD in 1972 with thesis advisor Kaarlo Virtanen in Helsinki.[2] Tukia is a professor at the University of Helsinki.

He made substantial contributions to the collective work of about a dozen mathematicians who proved the Seifert fiber space conjecture.[3] In 1992 he was an invited speaker with talk Generalizations of Fuchsian and Kleinian groups at the European Congress of European Mathematicians in Paris. In 1994 he was an invited speaker with talk A survey of Möbius groups at the International Congress of Mathematicians in Zurich.

Selected publications
  • "On two dimensional quasiconformal groups", Ann. Acad. Sci. Fennica, Ser. A, vol. 5, 1980, pp. 73–78
  • "A quasiconformal group not isomorphic to the Möbius group", Ann. Acad. Sci. Fennica, Ser. A, vol. 6, 1981, pp. 149–160
  • "The Hausdorff dimension of the limit set of a geometrically finite Kleinian groups", Acta Mathematica, vol. 152, 1984, pp. 127–140 doi:10.1007/BF02392194
  • "On limit sets of geometrically finite Kleinian groups", Mathematica Scandinavica, vol. 57, 1985, pp. 29–43, Online
  • "Differentiability and rigidity of Möbius groups", Inventiones Mathematicae, vol. 82, 1985, pp. 557–578 doi:10.1007/BF01388870
  • "Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group", Acta Mathematica, vol. 154, 1985, pp. 153–193
  • "On isomorphisms of geometrically finite Möbius groups", Pub. Math. IHES, vol. 61, 1985, pp. 171–214 doi:10.1007/BF02698805
  • "On quasiconformal groups", J. Anal. Math., vol. 46, 1986, pp. 318–346 doi:10.1007/BF02796595
  • "A rigidity theorem for Möbius groups", Inventiones Mathematicae, vol. 97, 1989, pp. 405–431 doi:10.1007/BF01389048
  • "The Hausdorff dimension of quasisymmetric mappings", Mathematica Scandinavica, vol. 65, 1989, pp. 152–160 JSTOR 24492095
  • "Mostow-rigidity and non-compact hyperbolic manifolds", Quart. J. Math., Oxford, vol. 42, 1991, pp. 219–226 doi:10.1093/qmath/42.1.221
  • "Convergence groups and Gromov's metric hyperbolic spaces". New Zealand Journal of Mathematics, vol. 23, 1994, pp. 157–187
  • "Teichmüller sequences on trajectories invariant under a Kleinian group", Journal d'Analyse Mathématique, vol. 99, 2006, pp. 35–87 doi:10.1007/BF02789442
  • "Limits of Teichmüller maps", Journal d'Analyse Mathematique, vol. 125, 2015, pp. 71–111 doi:10.1007/s11854-015-0003-7
  • with James W. Anderson, Kurt Falk: "Conformal measures associated to ends of hyperbolic n-manifolds", Quarterly Journal of Mathematics, vol. 58, 2007, pp. 1–15, Arxiv

References
  1. "Tukia, Pekka". wiki.helsinki.fi.
  2. Pekka Tukia at the Mathematics Genealogy Project
  3. Préaux, Jean-Philippe (2012). "A survey on Seifert fibre space conjecture". arXiv:1202.4142 [math.AT].
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