Contents

• Analysis in metric spaces
• Conformal dimension
• Sub-Riemannian geometry
• Iterated function systems and fractal geometry
• Nonlinear potential theory
• Geometric measure theory
• Sobolev mappings
• Quasihyperbolic geometry
• Hyperspaces
• Quasiregular mappings

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

   Abstract

2. Sets of minimal Hausdorff dimension for quasiconformal mappings, in Proc. Amer. Math. Soc. 128 (2000) 3361-3367.

   Abstract

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

   Abstract

4. Metric and geometric quasiconformality in Ahlfors regular Loewner spaces, in Conf. Geom. Dynam. 5 (2001) 21-73.

   Abstract

5. 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

6. 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

7. 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.

   Abstract

8. 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

9. Characterizations of snowflake metric spaces, with J.-M. Wu, in Ann. Acad. Sci. Fenn. Ser. A I, Math. 30 (2005) 313-336.

   Abstract

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

    Abstract

11. Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets, with J. M. Mackay and K. Wildrick, preprint, 2011.

    Abstract

1. Sets of minimal Hausdorff dimension for quasiconformal mappings in Proc. Amer. Math. Soc. 128 (2000) 3361-3367.

   Abstract

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

   Abstract

3. Conformal dimension of the antenna set, with C.J. Bishop, in Proc. Amer. Math. Soc. 129 (2001) 3631-3636.

   Abstract

4. Lowering the Assouad dimension by quasiconformal mappings, in Illinois J. Math. 45 (2001) 641-656.

   Abstract

5. 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.

   Abstract

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

   Abstract

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

   Abstract

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

1. 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

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

   Abstract

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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.

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

   Abstract

10. 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.

11. 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

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

    Abstract

13. 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

14. Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type, with N. Garofalo, in Bulletin London Math. Soc., 44 no. 2 (2012) 353-366.   

    Abstract

15. 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, preprint, 2011.

    Abstract

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

    Abstract

17. 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

18. 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

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

    Abstract

1. Smooth quasiregular maps with branching in Rⁿ, with R.P. Kaufman and J.-M. Wu, in Publ. Math IHES. 101 (2005) 209-241.

   Abstract

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

   Abstract

1. Conformal dimension of the antenna set, with C.J. Bishop, in Proc. Amer. Math. Soc. 129 (2001) 3631-3636.

   Abstract

2. 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

3. Smooth quasiregular maps with branching in Rⁿ, with R.P. Kaufman and J.-M. Wu, in Publ. Math IHES. 101 (2005) 209-241.

   Abstract

4. 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

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

   Abstract

6. 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

7. 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

8. Rectifiable curves in Sierpinski carpets, with E. Durand Cartagena, preprint, 2010, to appear in Indiana Univ. Math. J.

   Abstract

1. 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

2. 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

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

   Abstract

4. 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

5. 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

6. 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

7. Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type, with N. Garofalo, in Bulletin London Math. Soc., 44 no. 2 (2012) 353-366.   

   Abstract

1. 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

2. 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.

3. 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

4. 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

5. 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, preprint, 2011.

   Abstract

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

   Abstract

1. 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

2. 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

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

   Abstract

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

   Abstract

1. 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

2. 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

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

   Abstract

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

   Abstract

2. 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