Evolution Families and the Loewner Equation I: The Unit Disc

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dc.creatorBracci, Filippo
dc.creatorContreras, Manuel D.
dc.creatorDiaz-Madrigal, Santiago
dc.date2008-07-10
dc.date.accessioned2026-07-07T09:49:34Z
dc.date.available2026-07-07T09:49:34Z
dc.descriptionIn this paper we introduce a general version of the Loewner differential equation which allows us to present a new and unified treatment of both the radial equation introduced in 1923 by K. Loewner and the chordal equation introduced in 2000 by O. Schramm. In particular, we prove that evolution families in the unit disc are in one to one correspondence with solutions to this new type of Loewner equations. Also, we give a Berkson-Porta type formula for non-autonomous weak holomorphic vector fields which generate such Loewner differential equations and study in detail geometric and dynamical properties of evolution families.
dc.description41 pages
dc.identifierhttps://arxiv.org/abs/0807.1594
dc.identifierhttp://arxiv.org/abs/0807.1594
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164634
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.subject30C80, 34M15, 30D05
dc.titleEvolution Families and the Loewner Equation I: The Unit Disc
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