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Harmonic and Complex Analysis and its Applications pp 39–134Cite as

Birkhäuser

Classical and Stochastic Löwner–Kufarev Equations

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Abstract

In this paper we present a historical and scientific account of the development of the theory of the Löwner–Kufarev classical and stochastic equations spanning the 90-year period from the seminal paper by K. Löwner in 1923 to recent generalizations and stochastic versions and their relations to conformal field theory.

Mathematics Subject Classification (2000). Primary 01A70 ⋅ 30C35; Secondary 17B68 ⋅ 70H06 ⋅ 81R10

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Notes

  1. 1.

    I have also some personal interest to this story because me, Falkovich and Shein worked in different periods at the same Saratov State University. A. Vasil’ev

  2. 2.

    See also [20] for an extension of this notion to complex manifolds and with a complete different approach even in the unit disk. The construction of a Löwner chain associated with a given evolution family proposed there differs essentially from the one we used in [53, Theorems 1.3 and 1.6].

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  1. Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy

    Filippo Bracci

  2. Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092, Sevilla, Spain

    Manuel D. Contreras & Santiago Díaz-Madrigal

  3. Department of Mathematics, University of Bergen, 7803, Bergen, N-5020, Norway

    Alexander Vasil’ev

Authors
  1. Filippo Bracci
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  2. Manuel D. Contreras
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  3. Santiago Díaz-Madrigal
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  4. Alexander Vasil’ev
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Corresponding author

Correspondence to Filippo Bracci .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Bergen, Norway

    Alexander Vasil'ev

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© 2014 Springer International Publishing Switzerland

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Bracci, F., Contreras, M.D., Díaz-Madrigal, S., Vasil’ev, A. (2014). Classical and Stochastic Löwner–Kufarev Equations. In: Vasil'ev, A. (eds) Harmonic and Complex Analysis and its Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-01806-5_2

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