Classical and Stochastic Löwner–Kufarev Equations

  • Filippo BracciEmail author
  • Manuel D. Contreras
  • Santiago Díaz-Madrigal
  • Alexander Vasil’ev
Part of the Trends in Mathematics book series (TM)


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.


Brownian motion Conformal mapping Evolution family Integrable system Kufarev Löwner Pommerenke Schramm Subordination chain 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Filippo Bracci
    • 1
    Email author
  • Manuel D. Contreras
    • 2
  • Santiago Díaz-Madrigal
    • 2
  • Alexander Vasil’ev
    • 3
  1. 1.Dipartimento Di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Departamento de Matemática Aplicada II, Escuela Técnica Superior de IngenieríaUniversidad de SevillaSevillaSpain
  3. 3.Department of MathematicsUniversity of BergenBergenNorway

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