Articles

  1.  Quasiconformal distortion of the Assouad dimension and the classification of polynomial spirals, with E. K. Chrontsios Garitsis, preprint 2021. Available at https://arxiv.org/pdf/2112.02620.pdf
  2.  Conformal graph directed Markov systems on Carnot groups, with V. Chousionis and M. Urbański, Memoirs of the AMS. 266, no. 1291 (2020), 155+viii pages.                     
  3.    On uniform measures in the Heisenberg group, with V. Chousionis and V. Magnani, Advances in Math., 363, 106980 (2020), 42 pp.
  4.    Analysis in Metric Spaces, with M. Bonk, L. Capogna, P. Hajlasz and N. Shanmugalingam, Notices of the AMS, 67 no. 2 (2020), 253-256.
  5. Cantor set arithmetic, with J. Athreya and B. Reznick, Amer. Math. Monthly, 126, no. 1 (2019), 4–17.
  6.    Heisenberg quasiregular ellipticity, with K. Fässler and A. Lukyanenko, Rev. Mat. Iberoamericana, 35, no. 2 (2019), 471-520.
  7.    Geometry labs united: an invitation, with J. Athreya, D. Dumas, W. Goldman, S. Grigorian, R. Guzman, P. Hieronymi, S. Lawton, A. Lukyanenko and A. Wilson, Notices of the AMS, 65 no. 9 (2018), 1088-1094.
  8.   Heat content and horizontal mean curvature in the Heisenberg group, with J. Wang, Comm. PDE, 43 no. 3 (2018), 467-505.
  9.    Quasiconvexity in the Heisenberg group, with D. Herron and A. Lukyanenko, Geom. Dedicata, 192 (2018), 157-170.
  10.    A new proof of the C regularity of C2 conformal mappings on the Heisenberg group, with A. D. Austin, Colloq. Math., 150 (2017), 217-228.
  11.    Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the sub-Riemannian Heisenberg group, with Z. M. Balogh and E. Vecchi, Math. Z., 287 (2017), 1-38.    See also the erratum, Math. Z., 296 no. 1 (2020), 875-876.
  12.   Frequency of Sobolev dimension distortion of horizontal subgroups of Heisenberg groups, with Z. M. Balogh and K. Wildrick, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 17 (2017), 655-683.   
  13.   Quasiconformal mappings that highly distort dimensions of many parallel lines, with Z. M. Balogh and K. Wildrick, Ann. Acad. Sci. Fenn. Ser. A I Math., 42 (2017) 61-72.
  14.    Removable sets for homogeneous linear PDE in Carnot groups, with V. Chousionis J. Analyse Math., 128 no. 1 (2016) 215-238.
  15.    Marstrand’s density theorem in the Heisenberg group, with V. Chousionis Bull. London Math. Soc., 47 no. 5 (2015) 771-788.   
  16.    Removable sets for Lipschitz harmonic functions on Carnot groups, with V. Chousionis and V. Magnani, Calc. Var. PDE, 53 no. 3-4 (2015) 755-780.   
  17.    On transverse submanifolds and their measure, with V. Magnani and D. Vittone, J. Analyse Math., 125 (2015), 319-351.   
  18.   Homotopy groups of spheres and Lipschitz homotopy groups of the Heisenberg groups, with P. Hajlasz and A. Schikorra, Geom. Funct. Analysis, 24 (2014) 245-268.   
  19.    On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg group target, with N. DeJarnette, P. Hajlasz and A. Lukyanenko, Conf. Geom. Dynam., 18 (2014), 119-156.   
  20.    Grassmannian frequency of Sobolev dimension distortion, with Z. M. Balogh and P. Mattila, Comput. Methods Funct. Theory, 14 no. 2-3 (2014) 505-523.   
  21.   Dimension distortion by Sobolev mappings in foliated metric spaces, with Z. M. Balogh and K. Wildrick, Analysis and Geometry in Metric Spaces, 1 (2013) 232-254.   
  22.   Modulus and Poincaré inequalities on non-self-similar Sierpiński carpets, with J. M. Mackay and K. Wildrick, Geom. Funct. Analysis, 23 no. 3 (2013) 985-1034.   
  23.   Quasiregular maps and the conductivity equation in the Heisenberg group, with A. Isopoussu and K. Peltonen, In the Tradition of Ahlfors-Bers, VI AMS Contemp. Math. 590 (2013), 61-75.   
  24.    The effect of projections on dimension in the Heisenberg group with Z. M. Balogh, E. Durand Cartagena, K. Fässler, and P. Mattila, Rev. Mat. Iberoamericana, 29 no. 2 (2013), 382-432.   
  25.   Frequency of Sobolev and quasiconformal dimension distortion, with Z. M. Balogh and R. Monti, J. Math. Pures Appl., 99 no. 2 (2013), 125-149.   
  26.   Projection and slicing theorems in Heisenberg groups with Z. M. Balogh, K. Fässler, and P. Mattila, Advances in Mathematics, 231 no. 2 (2012), 569-604.   
  27.   Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type, with N. Garofalo, Bulletin London Math. Soc., 44 no. 2 (2012) 353-366.   
  28.    Rectifiable curves in Sierpiński carpets, with E. Durand Cartagena, Indiana Univ. Math. J. 60 (2011) 285-310.    See also the erratum
  29.    An Invitation to Cauchy-Riemann and Sub-Riemannian Geometries, with J.P. D’Angelo, Notices Amer. Math. Soc. 57 no. 2 (2010) 208-219.   
  30.    Exceptional sets for self-similar fractals in Carnot groups with Z. M. Balogh, R. Berger and R. Monti, Math. Proc. Cambridge Philos. Soc. 149 (2010) no. 1, 147-172.   
  31.    Convexity and horizontal second fundamental forms for hypersurfaces in Carnot groups, with L. Capogna and S.D. Pauls, Trans. Amer. Math. Soc. 362 (2010) 4045-4062.   
  32.   Helical CR structures and sub-Riemannian geodesics, with J.P. D’Angelo, Complex Var. Elliptic Equ. 54 (2009) 205-221.   
  33.    Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry in Carnot groups, with Z. M. Balogh and B. Warhurst, Advances in Mathematics 220 (2009) 560-619.   
  34.    Sobolev Peano cubes, with P. Hajlasz, Michigan Math. J. 56 (2008) 687-702.   
  35.    Gromov’s dimension comparison problem on Carnot groups, with Z. M. Balogh and B. Warhurst, C. R. Acad. Sci. Paris Ser. I, Math 346 (2008) 135-138.   
  36.    Global conformal Assouad dimension in the Heisenberg group, Conf. Geom. Dynam. 12 (2008) 32-57.   
  37.    Hyperbolic and quasisymmetric structure of hyperspaces, with L.V. Kovalev, In the Tradition of Ahlfors-Bers, IV , AMS Contemp. Math. 432 (2007), 151-166.   
  38.    Sharp weighted Young’s inequalities and Moser-Trudinger inequalities on groups of Heisenberg type and Grushin spaces , Potential Anal. 24 (2006) 357-384.   
  39.    Quasiconformal dimensions of self-similar sets, with J.-M. Wu, Rev. Mat. Iberoamericana 22 (2006) 205-258.   
  40.    Lifts of Lipschitz maps and horizontal fractals on the Heisenberg group, with Z. M. Balogh and R. Hofer-Isenegger, Erg. Theory. and Dynam. Systems 26 (2006) 621-651.   
  41.    Bi-Lipschitz embeddings of hyperspaces of compact sets Fund. Math. 187 (2005) 229-254.   
  42.    Smooth quasiregular maps with branching in R^n, with R.P. Kaufman and J.-M. Wu, Publ. Math IHES. 101 (2005) 209-241.   
  43.    Characterizations of snowflake metric spaces, with J.-M. Wu, Ann. Acad. Sci. Fenn. Ser. A I, Math. 30 (2005) 313-336.   
  44.   Hausdorff dimensions of self-similar and self-affine fractals in the Heisenberg group, with Z. M. Balogh, Proc. London Math. Soc. 91 (2005) 153-183.   
  45.    Counterexamples to Tischler’s strong form of Smale’s Mean Value Conjecture Bull. London Math. Soc. 37 (2005) 95-106.   
  46.   Dirichlet forms, Poincaré inequalities and the Sobolev spaces of Korevaar-Schoen, with P. Koskela and N. Shanmugalingam, Pot. Anal. 21 (2004) 241-262. 
  47. 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.   
  48.    Fundamental solution for the Q-Laplacian and sharp Moser-Trudinger inequality in Carnot groups, with Z. M. Balogh and J.J. Manfredi, J. Funct. Anal. 204 (2003) 35-49.   
  49.    Potential theory in Carnot groups, with Z. M. Balogh, Harmonic Analysis at Mount Holyoke (W. Beckner, A. Nagel, A. Seeger and H. F. Smith, eds.), AMS Contemp. Math. 320 (2003) 15-27.  
  50.   Polar coordinates in Carnot groups, with Z. M. Balogh, Math. Z. 241 (2002) 697-730. 
  51.    Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups, with Z. M. Balogh and I. Holopainen, Math. Ann. 324 (2002) 159-186.   
  52.    Quasihyperbolic boundary conditions and Poincaré domains, with P. Koskela and J. Onninen, Math. Ann. 323 (2002) 811-830.   
  53.    Quasihyperbolic boundary conditions and capacity: Hölder continuity of quasiconformal mappings, with P. Koskela and J. Onninen, Comm. Math. Helv. 76 (2001) 416-435.   
  54.    Lowering the Assouad dimension by quasiconformal mappings, Illinois J. Math. 45 (2001) 641-656.   
  55.   Locally minimal sets for conformal dimension, with C.J. Bishop, Ann. Acad. Sci. Fenn. Ser. A I Math. 26 (2001) 361-373.   
  56.    Conformal dimension of the antenna set, with C.J. Bishop, Proc. Amer. Math. Soc. 129 (2001) 3631-3636.
  57.    On the conformal Martin boundary of domains in metric spaces, with I. Holopainen and N. Shanmugalingam, 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.  
  58.    Sobolev classes of Banach space-valued functions and quasiconformal mappings, with J. Heinonen, P. Koskela and N. Shanmugalingam, J. Analyse Math. 85 (2001) 87-139.
  59.   Metric and geometric quasiconformality in Ahlfors regular Loewner spaces, Conf. Geom. Dynam. 5 (2001) 21-73.
  60.    Analytic properties of locally quasisymmetric mappings from Euclidean domains, Indiana Univ. Math. J. 49 (2000) 995-1016.  
  61.   Sets of minimal Hausdorff dimension for quasiconformal mappings, Proc. Amer. Math. Soc. 128 (2000) 3361-3367. 
  62.    Quasiconformality and quasisymmetry in metric measure spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 23 (1998) 525-548.