Et profilbilde

Professor
Pavel Gumenyuk { "honorific-suffix": "Professor", "fn": "Pavel Gumenyuk", "tel": "Telephone: +47 51831911", "email": "pavel.gumenyuk@uis.no" }

Faculty Faculty of Science and Technology
Department Department of Mathematics and Physics
Room KE E-529

Personal web-page

Please, visit my personal page.

 

Research fields

Complex Analysis, especially Geometric Function Theory. This includes:

  • Loewner Theory in simply and multiply connected domains;
  • Theory of univalent functions and quasiconformal extensions;
  • Applications to Holomorphic Dynamics and Mathematical Physics;
  • Boundary behaviour of holomorphic dynamical systems.

Selected publications

(with I. Prause) Quasiconformal extensions, Loewner chains, and the ?-Lemma. Anal. Math. Phys. 8(2018), No. 4, 621-635. DOI 10.1007/s13324-018-0247-3. URL: https://link.springer.com/article/10.1007/s13324-018-0247-3

 

(with D. Prokhorov) Value regions of univalent self-maps with two boundary fixed points, Ann. Acad. Sci. Fenn. Math. 43:1 (2018), 451-462. DOI 10.5186/aasfm.2018.4321; ArXiv: https://arxiv.org/pdf/1703.05835.pdf

 

Parametric representation of univalent functions with boundary regular fixed points, Constr. Approx. 46 (2017), 435-458. DOI 10.1007/s00365-017-9376-4, URL: https://link.springer.com/article/10.1007/s00365-017-9376-4

 

(with F. Bracci) Contact points and fractional singularities for semigroups of holomorphic self-maps in the unit disc, J. Anal. Math. 130 (2016), No.1, 185-217. DOI 10.1007/s11854-016-0034-8, URL: http://link.springer.com/article/10.1007/s11854-016-0034-8

 

(with F. Bracci, M.D.Contreras and S.Díaz-Madrigal) Boundary regular fixed points in Loewner Theory, Ann. Mat. Pura Appl. 194 (2015), No.1, 221-245. DOI 10.1007/s10231-013-0372-4, URL: http://link.springer.com/article/10.1007/s10231-013-0372-4

 

Angular and unrestricted limits of one-parameter semigroups in the unit disk, J. Math. Anal. Appl. 417 (2014), No.1, 200-224. DOI 10.1016/j.jmaa.2014.02.057, URL: http://dx.doi.org/10.1016/j.jmaa.2014.02.057

 

(with M.D.Contreras and S.Díaz-Madrigal) Loewner Theory in annulus I: evolution families and differential equations, Trans. Amer. Math. Soc. 365 (2013), 2505-2543. DOI 10.1090/S0002-9947-2012-05718-7, URL: http://dx.doi.org/10.1090/S0002-9947-2012-05718-7

 

(with M.D.Contreras and S.Díaz-Madrigal) Loewner chains in the unit disk. Rev. Mat. Iberoam. 26 (2010), 975-1012. URL: https://projecteuclid.org/euclid.rmi/1282913829

 

(with E. Grong and A. Vasil'ev) Matching univalent functions and conformal welding. Ann. Acad. Sci. Fenn. Math. 34 (2009), 303-314. URL: http://www.acadsci.fi/mathematica/Vol34/vol34.html

 

The list of ALL publications can be found HERE.

 

 

Research in progress

  • one-parameter semigroups and holomorphic self-maps with prescribed boundary regular fixed points;
  • quasiconformal extensions based on (generalizations of) Loewner's parametric representation method.
  •  

Work experience

Please, see my CV.

Scientific publications (from Cristin)

  • Gumenyuk, Pavel (2018). Becker’s criterion for quasiconformal extendibility and the λ-Lemma. Research Center for Pure and Applied Math.,Tohoku University; 2018-09-05 - 2018-09-07.
  • Gumenyuk, Pavel (2017). Loewner Theory: recent results and applications. University of Helsinki, Dept. of Mathematics and Statistics; 2017-10-12.
  • Gumenyuk, Pavel (2017). Value regions of univalent self-maps with two boundary fixed points. Universidad del Valle, Cali, Colombia; 2017-11-26 - 2017-12-01.
  • Gumenyuk, Pavel (2016). Parametric representation of univalent holomorphic self-maps of the unit disk. INdAM (Istituto Nazionale di Alta Matematica "F. Severi"); 2016-09-05 - 2016-09-09.
  • Gumenyuk, Pavel (2016). Parametric representations and quasiconformal extensions by means of modern Loewner Theory. St. Petersburg State University and Steklov Math. Institute; 2016-10-17 - 2016-10-20.
  • Gumenyuk, Pavel (2016). Quasiconformal extensions of holomorphic functions in the half-plane via chordal Loewner equation. Universitetet i Bergen; 2016-05-09 - 2016-05-14.
  • Gumenyuk, Pavel (2015). Loewner-type representation for conformal self-maps of the disk with prescribed boundary fixed points. University of Bergen;
  • Gumenyuk, Pavel (2015). Quasiconformal extensions via the chordal Loewner equation. Bar-Ilan Univ., ORT Braude College, Univ.of South Florida; 2015-05-10 - 2015-05-15.
  • Gumenyuk, Pavel (2014). Loewner-type Parametric Representation of univalent self-maps with given boundary regular fixed points. Tokyo Institute of Technology; 2014-11-22 - 2014-11-24.
  • Gumenyuk, Pavel (2014). Recent advances in Loewner Theory. University of Oslo; 2014-12-11 - 2014-12-12.