Ilkka Holopainen: Selected papers


  1. Nonlinear potential theory and quasiregular mappings on Riemannian manifolds.
    Ann. Acad. Sci. Fenn. Ser. A I Math. Diss. 74 (1990), 1--45.
  2. Positive solutions of quasilinear elliptic equations on Riemannian manifolds.
    Proc. London Math. Soc. 65 (1992), 651--672.
  3. A Picard type theorem for quasiregular mappings of Rn into n-manifolds with many ends, (with S. Rickman).
    Rev. Mat. Iberoamericana 8 (1992), 131--148.
  4. Quasiregular mappings of the Heisenberg group, (with S. Rickman).
    Math. Ann. 294 (1992), 625--643.
  5. Classification of Riemannian manifolds in nonlinear potential theory, (with S. Rickman).
    Potential Analysis 2 (1993), 37--66.
  6. Rough isometries and p-harmonic functions with finite Dirichlet integral.
    Rev. Mat. Iberoamericana 10 (1994), 143--176.
  7. Solutions of elliptic equations on manifolds with roughly Euclidean ends.
    Math. Z. 217 (1994), 459--477.
  8. Failure of the Denjoy theorem for quasiregular mappings in dimension $n \ge 3$, (with S. Rickman).
    Proc. Amer. Math. Soc. 124 (1996), 1783--1788.
  9. Quasiregular maps on Carnot groups, (with J. Heinonen).
    J. Geom. Anal. 7 (1997), 109--148.
  10. p-harmonic functions on graphs and manifolds, (with P.M. Soardi).
    Manuscripta mathematica 94 (1997), 95--110.
  11. A strong Liouville theorem for p-harmonic functions on graphs, (with P.M. Soardi).
    Ann. Acad. Sci. Fenn. Ser. A I Math. 22 (1997), 205--226,
  12. Ricci curvature, Harnack functions, and Picard type theorems for quasiregular mappings, (with S. Rickman).
    In Analysis and Topology (C. Andreian-Cazacu, O. Lehto, and Th. M. Rassias, eds.), World Scientific, Singapore, 1998, pp. 315--326.
  13. Volume growth, Green's functions, and parabolicity of ends.
    Duke Math. J. 97 (1999), 319--346.
  14. A sharp L^q-Liouville theorem for p-harmonic functions.
    Israel J. Math. 115 (2000), 363--379.
  15. Harmonic functions and volume growth of fingerless ends.
    Math. Z. 235 (2000), 259--273.
  16. Volume growth and parabolicity, (with P. Koskela).
    Proc. Amer. Math. Soc. 129 (2001), 3425-3435.
  17. On the conformal Martin boundary of domains in metric spaces,
    (with N. Shanmugalingam and J. T. Tyson).
    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.
  18. Harnack inequality and hyperbolicity for subelliptic p-Laplacians with applications to Picard type theorems,
    (with T. Coulhon and L. Saloff-Coste).
    Geom. Funct. Anal. 11 (2001), 1139-1191.
  19. Singular functions on metric measure spaces,
    (with N. Shanmugalingam).
    Collect. Math. 53 (2002), 313-332.
  20. Asymptotic Dirichlet problem for the p-Laplacian on Cartan-Hadamard manifolds.
    Proc. Amer. Math. Soc. 130 (2002), 3393-3400.
  21. Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups,
    (with Z.M. Balogh and J. T. Tyson).
    Math. Ann. 324 (2002) 1, 159-186.
  22. Quasiregular mappings and the p-Laplace operator.
    Contemporary Mathematics Vol. 338 (2003), 219-239.
  23. Mappings of finite distortion: Global homeomorphism theorem, (with Pekka Pankka).
    Ann. Acad. Sci. Fenn. Ser. A I Math. 29 (2004), 59-80.
  24. A big Picard theorem for quasiregular mappings into manifolds with many ends, (with Pekka Pankka).
    Proc. Amer. Math. Soc. 133 (2005), 1143-1150.
  25. p-Laplace operator, quasiregular mappings, and Picard-type theorems, (with Pekka Pankka).
    In Quasiconformal Mappings and their Applications (S. Ponnusamy, T. Sugawa, and M. Vuorinen, eds.), Narosa Publishing House, New Delhi-Chennai-Mumbai-Kolkata, 2007, pp. 117-150.
  26. Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces, (with Urs Lang and Aleksi Vähäkangas).
    Math. Ann. 339 (2007), 1, 101-134.
  27. Asymptotic Dirichlet problem on negatively curved spaces, (with Aleksi Vähäkangas).
    In Proceedings of the International Conference on Geometric Function Theory, Special Functions and Applications (ICGFT)
    (R. W. Barnard and S. Ponnusamy, eds.),
    J. Analysis 15 (2007), 63-110.
  28. p-Capacity and p-Hyperbolicity of Submanifolds, (with Steen Markvorsen and Vicente Palmer).
    Rev. Mat. Iberoamericana 25 (2009), 2, 709-738.
  29. Global comparison principles for the p-Laplace operator on Riemannian manifolds, (with Stefano Pigola and Giona Veronelli).
    Potential Analysis 34 (2011), 371-384.
  30. Nonsolvability of the asymptotic Dirichlet problem for the p-Laplacian on Cartan–Hadamard manifolds,
    Adv. Calc. Var., 9 (2016), no. 2, 163–185.
  31. Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds, (with J. Ripoll).
    Rev. Mat. Iberoamericana, 31 (2015), no. 3, 1107-1129.
  32. Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures, (with Jean-Baptiste Casteras and Esko Heinonen).
    J. Geom. Anal., 27 (2017), no. 2., 1106-1130.
  33. On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold,
    (with Jean-Baptiste Casteras and Jaime Ripoll).
    Potential Analysis, 47 (2017), no. 4., 485-501.
  34. Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems.
    (with Jean-Baptiste Casteras and Jaime Ripoll).
    Math. Z. 290 (2018), 221-250.
  35. Asymptotic Dirichlet problem for A-harmonic and minimal graph equations in Cartan-Hadamard manifolds.
    (with Jean-Baptiste Casteras and Jaime Ripoll).
    Communications in Analysis and Geometry, to appear.
  36. Dirichlet problem for f-minimal graphs. (with Jean-Baptiste Casteras and Esko Heinonen).
    Journal d’Analyse Mathématique, to appear.
  37. Existence and non-existence of minimal graphic and p-harmonic functions (with Jean-Baptiste Casteras and Esko Heinonen).
    Proc. Roy. Soc. Edinburgh Sect. A, to appear.

ilkka.holopainen@helsinki.fi