A Loewner Equation for Infinitely Many Slits

Marc Technau, Niclas Technau*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


It is well-known that the growth of a slit in the upper half-plane can be encoded via the chordal Loewner equation, which is a differential equation for schlicht functions with a certain normalisation. We prove that a multiple slit Loewner equation can be used to encode the growth of the union Γ of multiple slits in the upper half-plane if the slits have pairwise disjoint closures. Under certain assumptions on the geometry of Γ , our approach allows us to derive a Loewner equation for infinitely many slits as well.

Original languageEnglish
Pages (from-to)255-272
Number of pages18
JournalComputational Methods and Function Theory
Issue number2
StatePublished - 1 Jun 2017
Externally publishedYes


  • Chordal Loewner equation
  • Infinitely many slits
  • Loewner theory
  • Slit domain


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