Research supported by NSF Graduate and Postdoctoral Research Fellowships and NSF grants DMS-0228807, DMS-0555869 and DMS-0901620.

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.

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, vol. 259, Birkhauser, 2007.

2. Conformal dimension: theory and application with J. M. Mackay, University Lecture Series, vol. 54, American Mathematical Society, 2010.

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

2. PDF    Projection and slicing theorems in Heisenberg groups with Z. M. Balogh, K. Fässler, and P. Mattila, preprint, 2011.    Abstract

3. PDF    Quasiregular maps and the conductivity equation in the Heisenberg group, with A. Isopoussu and K. Peltonen, preprint, 2011.    Abstract

4. PDF    On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg group target, with N. DeJarnette, P. Hajlasz and A. Lukyanenko, preprint, 2011.    Abstract

5. PDF    Modulus and Poincare inequalities on non-self-similar Sierpinski carpets, with J. M. Mackay and K. Wildrick, preprint, 2011.    Abstract

6. Abstract    PDF    Frequency of Sobolev and quasiconformal dimension distortion, with Z. M. Balogh and R. Monti, preprint, 2010.    Abstract

7. PDF    The effect of projections on dimension in the Heisenberg group with Z. M. Balogh, E. Durand Cartagena, K. Fässler, and P. Mattila, to appear in Rev. Mat. Iberoamericana.    Abstract

8. PDF    Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type, with N. Garofalo, to appear in Bulletin London Math. Soc., doi:10.1112/blms/bdr102, published online Dec. 4 2011    Abstract

9. PDF    Rectifiable curves in Sierpinski carpets, with E. Durand Cartagena, to appear in Indiana Univ. Math. J.    Abstract

10. PDF    An Invitation to Cauchy-Riemann and Sub-Riemannian Geometries, with J.P. D'Angelo, Notices Amer. Math. Soc. 57 no. 2 (2010) 208-219.    Abstract

11. PDF    Exceptional sets for self-similar fractals in Carnot groups with Z. M. Balogh, R. Berger and R. Monti, in Math. Proc. Cambridge Philos. Soc. 149 (2010) no. 1, 147-172.    Abstract

12. PDF    Convexity and horizontal second fundamental forms for hypersurfaces in Carnot groups, with L. Capogna and S.D. Pauls, in Trans. Amer. Math. Soc. 362 (2010) 4045-4062.    Abstract

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

14. 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.    Abstract

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

16. 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.    Abstract

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

18. 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.    Abstract

19. 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.    Abstract

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

21. 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.    Abstract

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

23. 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.    Abstract

24. 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.    Abstract

25. 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.    Abstract

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

27. 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.    Abstract

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

29. 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.    Abstract

30. 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.    Abstract

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

32. 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.    Abstract

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

34. 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.    Abstract

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

36. 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.    Abstract

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

38. 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.    Abstract

39. 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.    Abstract

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

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

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

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

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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