Roth, Oliver

I am a complex guy: geometric function theory, conformal geometry, Loewner evolution

Preprints

• Hyperbolic distortion and conformality at the boundary,
  (with Pavel Gumenyuk , Maria Kourou and Annika Moucha)
  arxiv.org:2410.13865

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• The strong form of the Ahlfors-Schwarz lemma at the boundary and a rigidity result for Liouville's equation
  (with Filippo Bracci and Daniela Kraus)
  Israel J. Math., to appear
  arxiv.org:2310.05521

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• Spectral theory of the invariant Laplacian on the disk and the sphere - a complex analysis approach
  (with Michael Heins and Annika Moucha)
  Canadian J. Math., to appear
  arxiv.org:2312.12900

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• Peschl-Minda derivatives and convergent Wick star products on the disk, the sphere and beyond
  (with Michael Heins, Annika Moucha and Toshiyuki Sugawa)
  J. d'Anal. Math., to appear
  arxiv.org:2308.01101

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• Strict Wick-type deformation quantization on Riemann surfaces: Rigidity and Obstructions
  (with Daniela Kraus, Sebastian Schleißinger and Stefan Waldmann)
  arxiv.org:2308.01114

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Publications

• Function Theory off the complexified unit circle: Fréchet space structure and automorphisms,
  (with Michael Heins and Annika Moucha)
  Ann. Fenn. Math. 49 no.1, 257-280, 2024  Link
  arxiv:2308.01107

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• The angular derivative problem for petals of one-parameter semigroups of the unit disk
  (with Pavel Gumenyuk and Maria Kourou)
  Rev. Mat. Iberoam. 2024, Link
   arxiv.org:2303.00700

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• A new Schwarz-Pick lemma at the boundary and rigidity of holomorphic maps,
  (with Filippo Bracci and Daniela Kraus)
  Adv. Math. 432 Article 109262, 2023, Link
  arXiv:2003.02019

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• Geometric Versions of Schwarz's Lemma for Spherically Convex Functions,
  (with Maria Kourou)
  Canadian J. Math. 75 no. 6, 1780-1799, 2023, Link
  arXiv:2204.01577

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• Semigroup-fication of univalent self-maps of the unit disc,
  (with Filippo Bracci)
  Ann. Inst. Fourier  73 no. 1,  251-277, 2023, Link
  arXiv:2002.08252

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• Convergent Star Products on Cotangent Bundles of Lie Groups,
  (with Michael Heins und Stefan Waldmann)
  Math. Ann.  386 no. 1-2, 151-206, 2023,  Link
  arXiv:2107.14624

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• The Nehari-Schwarz lemma and infinitesimal boundary rigidity of bounded holomorphic functions
  Stud. Univ. Babeș-Bolyai 67 no.2, 285-294, 2022

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• A sharp Bernstein-type inequality and application to the Carleson embedding theorem with matrix weights
  (with Daniela Kraus and Annika Moucha)
  Anal. Math. Phys., 12 no. 2, Paper No. 46, 2022, Open Access doi.org/10.1007/s13324-021-00639-5
  arXiv:2110.10730

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• On the squeezing function for finitely connected planar domains,
  (with Pavel Gumenyuk)
  Math. Ann.  384 no. 1-2, 551-574, 2022, doi.org/10.1007/s00208-021-02296-2
  arXiv:2011.13734

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• Blow-up solutions of Liouville's equation and quasi-normality
  (with Jürgen Grahl and Daniela Kraus)­
  Comp. Methods Funct. Theory,  20 no 3-4, 677-692, 2020
  arXiv:2006.04925

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• A Schwarz lemma for locally univalent meromorphic functions,
  (with Richard Fournier and Daniela Kraus) 
  Proc. Amer. Math. Soc., 148 no. 9, 3859-3870, 2020.
  arXiv:1902.07242

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• A convergent star product on the Poincaré disc,
  (with Matthias Schötz, Stefan Waldmann and Daniela Kraus)
   J. Funct. Anal., 277 no. 8, 2734-2771, 2019.
  arXiv:1803.0276

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• Jack and Julia,
  (with Richard Fournier)
  Contemp. Math. 743,  213-216, 2020.

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• Universal locally univalent functions and universal conformal metrics with constant curvature,
  (with Daniel Pohl)
  Constr. Approx. 50, 145–165, 2019.
  arXiv:1709.10454

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• Is there a Teichmüller principle in higher dimensions?
  in: Geometric Function Theory in Higher Dimension, Springer INdAM 26, 87-105, 2017.
  arXiv:1704.07418

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  Support points and the Bieberbach conjecture in higher dimension,
  (with Filippo Bracci)
  in Complex Analysis and Dynamical Systems, Trends Math. Springer, 67-79, 2018.

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• Strong submultiplicativity of the Poincaré metric,
  (with Daniela Kraus)
  J. Anal. 24, 39-50, 2016.

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• 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,
  (with Daniela Kraus)
  Constr. Approx. 43, 47-69, 2016.

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• Pontryagin's maximum principle for the Loewner equation in higher dimensions,
  Canad. J. Math. 67 (4), 942-960, 2015. (arXiv:1402.6896)

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• Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation,
  (with Sebastian Schleißinger)
  Bull. London Math. Soc. 46, 1099-1109, 2014.

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• The Schramm-Loewner equation for multiple slits,
  (with Sebastian Schleißinger)
  J. d'Analyse Math. 131, 73-99, 2017.
  (see arXiv:1311.0672)

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• Composition and decomposition of indestructible Blaschke products,
  (with Daniela Kraus)
  Comp. Methods Funct. Theory 13 No. 2, 253-262, 2013.

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• Maximal Blaschke products,
  (with Daniela Kraus)
  Adv. Math. 241, 58-78, 2013.

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• Critical points, the Gauss curvature equation and Blaschke products,
  (with Daniela Kraus)
  Fields Institute Comm. 65, 133-157, 2012.

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• On Beurling's boundary value problem in Circle Packing,
  (with Daniela Kraus and Elias Wegert)
  Complex Variables and Elliptic Equations 57 No. 2-4, 397-410, 2012.

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• Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky,
  (with Daniela Kraus and Toshiyuki Sugawa)
  Math. Z. 267 No. 3-4, 851-868, 2011.

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• Conformal Metrics,
  (with Daniela Kraus)
  Ramanujan Math. Society, Lecture Notes Series 19, 41-83, 2013.
  see arXiv:0805.2235

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• The Loewner and Hadamard variations,
  (with Eric Schippers)
  Illinois J. Math. 52 No. 4, 1399-1415, 2008.

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• On the isolated singularities of the solutions of the Gaussian curvature equation for nonnegative curvature,
  (with Daniela Kraus)
  J. Math. Anal. Appl. 345 No. 2, 628-631, 2008.

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• Beurling's free boundary value problem in conformal geometry,
  (with Florian Bauer, Daniela Kraus and Elias Wegert)
  Israel Journal Math. 180, 223-254, 2010

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• The behaviour of solutions of the Gaussian curvature equation near an isolated boundary point,
  (with Daniela Kraus)
  Math. Proc. Cambridge Phil. Soc. 145, 643-667, 2008.

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• A note on generating functions for Hausdorff moment sequences,
  (with Stephan Ruscheweyh and Luis Salinas)
  Proc. Amer. Math. Soc. 136 No. 9, 3171-3176, 2008.

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• Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem,
  (with Daniela Kraus)
  J. London Math. Soc. 77 No. 1, 183-202, 2008.

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• An extension of Lewis's lemma, renormalization of harmonic and analytic functions, and normal families,
  (with Jürgen Grahl)
  Math. Nachr. 282 No. 4, 540-551, 2009.

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• A boundary version of Ahlfors' Lemma, locally complete conformal metrics and conformally invariant reflection principles for analytic maps,
  (with Daniela Kraus and Stephan Ruscheweyh)
  J. d'Analyse Math. 101, 219-256, 2007.

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• A sharp inequality for the logarithmic coefficients of univalent functions,
  Proc. Amer. Math. Soc. 135 No. 7, 2051-2054, 2007.

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• A general conformal geometric reflection principle,
  Trans. Amer. Math. Soc. 359 No. 6, 2501-2529, 2007.

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• Weighted distortion in conformal mapping in Euclidean, hyperbolic and elliptic geometry,
  (with Daniela Kraus)
  Ann. Acad. Sci. Fenn. Math. 31, 111-130, 2006.

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• A generalization of Bertilsson's theorem,
  (with Karl-Joachim Wirths)
  Bull. Belg. Math. Soc. 12, 53-63, 2005.

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• Helmut Grunsky. Collected Papers,
  (with Stephan Ruscheweyh)
  Heldermann Verlag, 530 pages, ISBN 3-88538-501-5, 2004.

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• On the local extremum property of the Koebe function,
  (with Dmitri Prokhorov)
  Math. Proc. Cambr. Phil. Soc. 136, 301-312, 2004.

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• Distortion theorems for bounded univalent functions,
  Analysis 23, 347-369, 2003.

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• A nonlinear extremal problem for Bloch functions with applications to geometric function theory,
  Arch. Math. 81, 655-665, 2003.

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• On the radius of convexity of linear combinations of univalent functions and their derivatives,
  (with Richard Greiner)
  Math. Nachr. 254-255, 153-164, 2003.

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• Taylor coefficients of negative powers of schlicht functions,
  (with Karl-Joachim Wirths)
  Computational Methods and Function Theory 1 no. 2, 521-533, 2001.

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• A distortion theorem for bounded univalent functions,
  Ann. Acad. Sci. Fenn. Math. 27, 257-272, 2002.

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• On support points of univalent functions and a disproof of a conjecture of Bombieri,
  (with Richard Greiner )
  Proc. Amer. Math. Soc. 129 no. 12, 3657-3664, 2001.

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• A coefficient problem for univalent functions related to two-point distortion theorems,
  (with Richard Greiner )
  Rocky Mountain J. Math. 31 no. 1, 261-283, 2001.

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• Pontryagin's maximum principle in geometric function theory,
  Complex Variables 41, 391-426, 2000.

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• A remark on the Loewner differential equation,
  Proceedings of the CMFT'97 in Nicosia, Cyprus (1997), Computational Methods and Function Theory 1997, N. Papamichael, St. Ruscheweyh, E. Saff (eds.), World Scientific, 1999, 461-469.

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• On the Taylor coefficients for powers of the derivative of univalent functions,
  Journal of Analysis 6 , 131-138, 1998.  

Auf den Tod eines kleinen Kindes

Jetzt bist du schon gegangen, Kind,
Und hast vom Leben nichts erfahren,
Indes in unsern welken Jahren
Wir Alten noch gefangen sind.

Ein Atemzug, ein Augenspiel,
Der Erde Luft und Licht zu schmecken,
War dir genug und schon zuviel;
Du schliefest ein, nicht mehr zu wecken.

Vielleicht in diesem Hauch und Blick
Sind alle Spiele, alle Mienen
Des ganzen Lebens dir erschienen,
Erschrocken zogst du dich zurück.

Vielleicht wenn unsre Augen, Kind,
Einmal erlöschen, wird uns scheinen,
Sie hätten von der Erde, Kind,
Nicht mehr gesehen als die deinen.

Hermann Hesse

Complex Analysis and Operator Theory