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Complex Analysis


Selected Publications

  • Filippo Bracci, Daniela Kraus and Oliver Roth
    A new Schwarz-Pick lemma at the boundary and rigidity of holomorphic maps,
    Adv. Math.  to appear see arXiv:2003.02019
  • Filippo Bracci and Oliver Roth
    Semigroup-fication of univalent self-maps of the unit disc,
    Ann. Inst. Fourier  73 no. 1,  251-277, 2023, Link
    see arXiv:2002.08252
  • Daniela Kraus, Annika Moucha and Oliver Roth
    A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights
    Anal. Math. Phys., 12 no. 2, Paper No. 46, 2022, Open Access
    see arXiv:2110.10730
  • Michael Heins, Oliver Roth and Stefan Waldmann
    Convergent Star Products on Cotangent Bundles of Lie Groups,
    Math. Ann.  386 no. 1-2, 151-206, 2023,
    see arXiv:2107.14624
  • Oliver Roth and Pavel Gumenyuk
    On the squeezing function for finitely connected planar domains,
    Math. Ann.  384 no. 1-2, 551-574, 2022,
    see arXiv:2011.13734
  • Richard Fournier, Daniela Kraus and Oliver Roth
    A Schwarz lemma for locally univalent meromorphic functions,
    Proc. Amer. Math. Soc., 148 no. 9, 3859-3870, 2020. (arXiv:1902.07242)
  • Daniela Kraus, Oliver Roth, Matthias Schötz and Stefan Waldmann
    A convergent star product on the Poincaré disc,
     J. Funct. Anal., 277 no. 8, 2734-2771, 2019. 
  • Jürgen Grahl, Shahar Nevo
    Quasi-normality induced by differential inequalities
    Bull. Lond. Math. Soc. 50, 73-84, 2018
  • Oliver Roth, Sebastian Schleißinger
    The Schramm-Loewner equation for multiple slits
    J. d'Analyse Math.131,73-99, 2017
  • Daniela Kraus, Oliver Roth
    Sharp lower bounds for the hyperbolic metric of the complement of a closed subset of the unit circle and theorems of Schwarz-Pick-, Schottky- and Landau-type for analytic functions
    Constr. Approx. 43, 47-69, 2016
  • Oliver Roth
    Pontryagin's maximum principle for the Loewner equation in higher dimensions
    Canad. J. Math. 67 (4), 942-960, 2015
  • Daniela Kraus, Oliver Roth
    Maximal Blaschke products
    Adv. Math. 241, 58-78, 2013
  • Daniela Kraus
    Critical sets of bounded analytic functions, zero sets of Bergman spaces and nonpositive curvature
    Proc. London Math. Soc. 106 No. 4, 931-956, 2013
  • Daniela Kraus, Oliver Roth, Stephan Ruscheweyh
    A boundary version of Ahlfors' Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps
    J. d'Analyse Math. 101, 219-256, 2007
  • Oliver Roth
    A general conformal geometric reflection principle,
    Trans. Amer. Math. Soc. 359 No. 6, 2501-2529, 2007