Kai Rajala

Professor
Office: MaD 358
Phone: (040) 805 3465
Email: kai.i.rajala 'at' jyu.fi

Opetus/Teaching

  • MATA181 Vektoricalculus 1, Syksy 2017
  • MATA182 Vektoricalculus 2, Syksy 2017
  • MATJ1200 Seminar on Analysis in Metric Spaces, Fall 2017

    Aiemmat kurssit/Previous courses

  • MATA221 Algebra 1: Ryhmät, Kevät 2017
  • MATS226 Quasiconformal Mappings in the plane, Fall 2016
  • MATA222 Algebra 1B Kevät, 2016
  • MATA221 Algebra 1A Kevät, 2016
  • MATA222 Algebra 1B Kevät, 2015
  • MATA221 Algebra 1A Kevät, 2015
  • MATS110 Mitta- ja integraaliteoria (osat 1 ja 2), Kesä 2014
  • MATS110 Mitta- ja integraaliteoria (osat 1 ja 2), Syksy 2013
  • MATA140 Johdatus diskreettiin matematiikkaan (sijaisluennoitsija), Syksy 2013
  • MATS120 Kompleksianalyysi (osat 1 ja 2), Kevät 2013
  • MATS110 Mitta- ja integraaliteoria (osat 1 ja 2), Syksy 2012

    Publications and Preprints

    1. Quasispheres and metric doubling measures, Proc. Amer. Math. Soc., to appear. preprint (with A. Lohvansuu and M. Rasimus)
    2. Uniformization of two-dimensional metric surfaces, Invent. Math., 207 (2017), no. 3, 1301--1375. preprint
    3. Wolfe's theorem for weakly differentiable cochains, J. Funct. Anal., 268 (2015), no. 8, 2261--2297. (with C. Petit and S. Wenger) preprint
    4. Exponential integrability of mappings of finite distortion, Rev. Mat. Iberoam., 31 (2015), no. 4, 1459--1476. (with T. Äkkinen) preprint
    5. Quasiregular ellipticity of open and generalized manifolds, Comput. Methods Funct. Theory. Special volume dedicated to the memory of Fred Gehring, 14 (2014), no. 2-3, 383--398. (with P. Pankka and J-M. Wu) preprint
    6. An upper gradient approach to weakly differentiable cochains, J. Math. Pures Appl., 100 (2013), no. 6, 868--906. (with S. Wenger) preprint
    7. Bonnesen's inequality for John domains in R^n, J. Funct. Anal., 263 (2012), no. 11, 3617--3640. (with X. Zhong) preprint
    8. Optimal assumptions for discreteness, Arch. Rational Mech. Anal., 207 (2013), 775--783. (with S. Hencl) preprint
    9. Mappings of finite distortion and asymmetry of domains, Ann. Acad. Sci. Fenn. Math., 38 (2013), no. 1, 367--375. (with G. Moscariello and A. Passarelli di Napoli) preprint
    10. Openness and discreteness for mappings of finite distortion, Rend. Lincei Mat. Appl., 23 (2012), 1--7. (with S. Hencl) preprint
    11. Mappings of finite distortion: decay of the Jacobian, J. Geom. Anal., 22 (2012), no. 4, 964--976. (with P. Koskela and J. Onninen) preprint
    12. Quantitative isoperimetric inequalities and homeomorphisms with finite distortion, Ann. Sc. Norm. Super. Pisa, 11 (2012), no. 1, 177--196. pdf
    13. Quasiconformal extension fields, Calc. Var. Partial Differential Equations, 42 (2011), no. 1--2, 73--91. (with P. Pankka) pdf
    14. Quasiregularly elliptic link complements, Geom. Dedicata, 154 (2011), no. 1, 1--8. (with P. Pankka) pdf
    15. Reshetnyak's theorem and the inner distortion, Pure Appl. Math. Q., Special issue in honor of Frederick W. Gehring, 7 (2011), no. 2, 411--424. pdf
    16. Remarks on the Iwaniec-Sverak conjecture, Indiana Univ. Math. J., 59 (2010), no. 6, 2027--2040. pdf
    17. Invertibility of Sobolev mappings under minimal hypotheses, Ann. Inst. H. Poincare Anal. Non Lineaire, 27 (2010), no. 2, 517--528. (with L. Kovalev and J. Onninen) pdf
    18. Quasiconformal frames, Arch. Rational Mech. Anal., 196 (2010), no. 3, 839--866. (with J. Heinonen and P. Pankka) pdf
    19. Quasiregular mappings to generalized manifolds, J. Anal. Math., 109 (2009), 33--79. (with J. Onninen) pdf
    20. Sharp exponential integrability for traces of monotone Sobolev functions, Nagoya Math. J., 192 (2008), 137--149. (with P. Pankka and P. Poggi-Corradini) pdf
    21. Radial limits of quasiregular local homeomorphisms, Amer. J. Math., 130 (2008). no. 1, 269--289. pdf
    22. An egg-yolk principle and exponential integrability for quasiregular mappings, J. London Math. Soc., 76 (2007), no. 2, 531--544. (with P. Poggi-Corradini) pdf
    23. Bloch's theorem for mappings of bounded and finite distortion, Math. Ann., 339 (2007), no. 2, 445--460. pdf
    24. Surface families and boundary behavior of quasiregular mappings, Illinois J. Math., 49 (2005), no. 4, 1145--1153. pdf
    25. Distortion of quasiconformal and quasiregular mappings at extremal points, Michigan Math. J., 53 (2005), no. 2, 447--458. pdf
    26. The local homeomorphism property of spatial quasiregular mappings with distortion close to one, Geom. Funct. Anal., 15 (2005), no. 5, 1100--1127. pdf
    27. Mappings of finite distortion: the Rickman-Picard theorem for mappings of finite lower order, J. Anal. Math., 94 (2004), 235--248. pdf
    28. Mappings of finite distortion: Removability of Cantor sets, Ann. Acad. Sci. Fenn. Math., 29 (2004), no. 2, 269--281. pdf
    29. A remark on Poincare inequalities on metric measure spaces, Math. Scand., 95 (2004), no. 2, 299--304. (with S. Keith) pdf
    30. Mappings of finite distortion: Removable singularities for locally homeomorphic mappings, Proc. Amer. Math. Soc., 132 (2004), no. 11, 3251--3258. pdf
    31. A lower bound for the Bloch radius of K-quasiregular mappings, Proc. Amer. Math. Soc., 132 (2004), no. 9, 2593--2601. pdf
    32. Mappings of finite distortion: Injectivity radius of a local homeomorphism, pp 169--174 in 'Future Trends in Geometric Function Theory RNC Workshop Jyväskylä 2003', Report 92, Department of Mathematics and Statistics, University of Jyväskylä 2003. (with P. Koskela and J. Onninen)
    33. Mappings of finite distortion: Removable singularities, Ph. D. Thesis, Report 91, Department of Mathematics and Statistics, University of Jyväskylä 2003. pdf
    34. Mappings of finite distortion: Removable singularities, Israel J. Math., 136 (2003), 269--283. (with P. Koskela) pdf
    35. Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces, J. Funct. Anal., 202 (2003), no. 1, 147--173. (with P. Koskela and N. Shanmugalingam) pdf