University of Illinois at Urbana-Champaign

PUBLICATIONS AND PREPRINTS OF J. T. TYSON

Research supported by NSF Graduate and Postdoctoral Research Fellowships and NSF grants DMS-0228807 and DMS-0555869.

Any opinions, findings, conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Books and Monographs

  1. An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem with L. Capogna, D. Danielli, and S.D. Pauls, Progress in Mathematics, 259, Birkhauser, 2007.

Papers

  1. Density of Lipschitz maps in Sobolev spaces with Heisenberg group target (title subject to change), with Piotr Hajlasz, in preparation.

  2. Lipschitz and Holder Peano cubes and highly regular surjections between Carnot groups (title subject to change), with Piotr Hajlasz, in preparation.

  3. Exceptional sets for self-similar fractals in Carnot groups with Z. M. Balogh, Reto Berger and Roberto Monti, preprint, 2009.

  4. Abstract    PDF    Sobolev Peano cubes, with Piotr Hajlasz, in Michigan Math. J. 56 (2008) 687-702.

  5. Abstract    PDF    Helical CR structures and sub-Riemannian geodesics, with J.P. D'Angelo, in Complex Var. Elliptic Equ. 54 (2009) 205-221.

  6. Abstract    PS    PDF    Convexity and horizontal second fundamental forms for hypersurfaces in Carnot groups, with L. Capogna and S.D. Pauls, preprint, May 2006, to appear in Trans. Amer. Math. Soc.

  7. Abstract    PDF    Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry in Carnot groups, with Z.M. Balogh and B. Warhurst, in Advances in Mathematics 220 (2009) 560-619.

  8. Abstract    PDF    Gromov's dimension comparison problem on Carnot groups, with Z.M. Balogh and B. Warhurst, in C. R. Acad. Sci. Paris Ser. I, Math 346 (2008) 135-138.

  9. Abstract    PDF    Global conformal Assouad dimension in the Heisenberg group, in Conf. Geom. Dynam. 12 (2008) 32-57.

  10. Abstract    PS    PDF    Hyperbolic and quasisymmetric structure of hyperspaces, with L.V. Kovalev, in In the Tradition of Ahlfors-Bers, IV , AMS Contemp. Math. 432 (2007), 151-166.

  11. Abstract    PDF    Sharp weighted Young's inequalities and Moser-Trudinger inequalities on groups of Heisenberg type and Grushin spaces in Potential Anal. 24 (2006) 357-384.

  12. Abstract    PDF    Quasiconformal dimensions of self-similar sets, with J.-M. Wu, in Rev. Mat. Iberoamericana 22 (2006) 205-258.

  13. Abstract    PDF    Lifts of Lipschitz maps and horizontal fractals on the Heisenberg group, with Z.M. Balogh and R. Hofer-Isenegger, in Erg. Theory. and Dynam. Systems 26 (2006) 621-651.

  14. Abstract    PDF    Bi-Lipschitz embeddings of hyperspaces of compact sets in Fund. Math. 187 (2005) 229-254.

  15. Abstract    PS    PDF    Smooth quasiregular maps with branching in R^n, with R.P. Kaufman and J.-M. Wu, in Publ. Math IHES. 101 (2005) 209-241.

  16. Abstract    PS/PDF/DVI    Characterizations of snowflake metric spaces, with J.-M. Wu, in Ann. Acad. Sci. Fenn. Ser. A I, Math. 30 (2005) 313-336.

  17. Abstract    PDF    Hausdorff dimensions of self-similar and self-affine fractals in the Heisenberg group, with Z.M. Balogh, in Proc. London Math. Soc. 91 (2005) 153-183.

  18. Abstract    PDF    Counterexamples to Tischler's strong form of Smale's Mean Value Conjecture in Bull. London Math. Soc. 37 (2005) 95-106.

  19. Abstract    PDF    Dirichlet forms, Poincaré inequalities and the Sobolev spaces of Korevaar-Schoen, with P. Koskela and N. Shanmugalingam, in Pot. Anal. 21 (2004) 241-262.

  20. Abstract    PS    Quasiconformal maps on metric spaces: questions and conjectures, in Future Trends in Geometric Function Theory: Rolf Nevanlinna Colloquium Workshop, Juväskylä, 2003 (D. Herron, ed.), Report. Univ. Jyväskylä 92 (2003) 249-262.

  21. Abstract    PDF    Fundamental solution for the Q-Laplacian and sharp Moser-Trudinger inequality in Carnot groups, with Z.M. Balogh and J.J. Manfredi, in J. Funct. Anal. 204 (2003) 35-49.

  22. Abstract    PS    PDF    Potential theory in Carnot groups, with Z.M. Balogh, in Harmonic Analysis at Mount Holyoke (W. Beckner, A. Nagel, A. Seeger and H. F. Smith, eds.), AMS Contemp. Math. 320 (2003) 15-27.

  23. Abstract    PDF    Polar coordinates in Carnot groups, with Z.M. Balogh, in Math. Z. 241 (2002) 697-730.

  24. Abstract    PDF    Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups, with Z.M. Balogh and I. Holopainen, in Math. Ann. 324 (2002) 159-186.

  25. Abstract    PDF    Quasihyperbolic boundary conditions and Poincaré domains, with P. Koskela and J. Onninen, in Math. Ann. 323 (2002) 811-830.

  26. Abstract    PDF    Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings, with P. Koskela and J. Onninen, in Comm. Math. Helv. 76 (2001) 416-435.

  27. Abstract    PS/PDF    Lowering the Assouad dimension by quasiconformal mappings, in Illinois J. Math. 45 (2001) 641-656.

  28. Abstract    PS/PDF/DVI    Locally minimal sets for conformal dimension, with C.J. Bishop, in Ann. Acad. Sci. Fenn. Ser. A I Math. 26 (2001) 361-373.

  29. Abstract    PS/PDF/DVI    Conformal dimension of the antenna set, with C.J. Bishop, in Proc. Amer. Math. Soc. 129 (2001) 3631-3636.

  30. Abstract    PS    On the conformal Martin boundary of domains in metric spaces, with I. Holopainen and N. Shanmugalingam, in Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday (J. Heinonen, T. Kilpeläinen, and P. Koskela, eds.), Report. Univ. Jyväskylä 83 (2001) 147-168.

  31. Abstract    PS    PDF    Sobolev classes of Banach space-valued functions and quasiconformal mappings, with J. Heinonen, P. Koskela and N. Shanmugalingam, in J. Analyse Math. 85 (2001) 87-139.

  32. Abstract    PS/PDF/DVI    Metric and geometric quasiconformality in Ahlfors regular Loewner spaces in Conf. Geom. Dynam. 5 (2001) 21-73.

  33. Abstract    PDF    Analytic properties of locally quasisymmetric mappings from Euclidean domains, in Indiana Univ. Math. J. 49 (2000) 995-1016.

  34. Abstract    PS/PDF/DVI    Sets of minimal Hausdorff dimension for quasiconformal mappings in Proc. Amer. Math. Soc. 128 (2000) 3361-3367.

  35. Abstract    PS/DVI    Quasiconformality and quasisymmetry in metric measure spaces, in Ann. Acad. Sci. Fenn. Ser. A I Math. 23 (1998) 525-548.

Lecture Notes

  1. Lecture notes    Notes on a theorem of Jeff Cheeger, lecture notes from a course given by Juha Heinonen at the University of Michigan in Spring 1999.

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