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- Loewner_differential_equation abstract "In mathematics, the Loewner differential equation, or Loewner equation, is an ordinary differential equation discovered by Charles Loewner in 1923 in complex analysis and geometric function theory. Originally introduced for studying slit mappings (conformal mappings of the open disk onto the complex plane with a curve joining 0 to ∞ removed), Loewner's method was later developed in 1943 by the Russian mathematician Pavel Parfenevich Kufarev (1909–1968). Any family of domains in the complex plane that expands continuously in the sense of Carathéodory to the whole plane leads to a one parameter family of conformal mappings, called a Loewner chain, as well as a two parameter family of holomorphic univalent self-mappings of the unit disk, called a Loewner semigroup. This semigroup corresponds to a time dependent holomorphic vector field on the disk given by a one parameter family of holomorphic functions on the disk with positive real part. The Loewner semigroup generalizes the notion of a univalent semigroup. The Loewner differential equation has led to inequalities for univalent functions that played an important role in the solution of the Bieberbach conjecture by Louis de Branges in 1985. Loewner himself used his techniques in 1923 for proving the conjecture for the third coefficient. The Schramm-Loewner equation, a stochastic generalization of the Loewner differential equation discovered by Oded Schramm in the late 1990s, has been extensively developed in probability theory and conformal field theory.".
- Loewner_differential_equation wikiPageID "34134544".
- Loewner_differential_equation wikiPageLength "12417".
- Loewner_differential_equation wikiPageOutDegree "33".
- Loewner_differential_equation wikiPageRevisionID "637103466".
- Loewner_differential_equation wikiPageWikiLink Carathxc3xa9odorys_theorem_(conformal_mapping).
- Loewner_differential_equation wikiPageWikiLink Carathéodory_kernel_theorem.
- Loewner_differential_equation wikiPageWikiLink Category:Complex_analysis.
- Loewner_differential_equation wikiPageWikiLink Cauchy–Schwarz_inequality.
- Loewner_differential_equation wikiPageWikiLink Charles_Loewner.
- Loewner_differential_equation wikiPageWikiLink Complex_analysis.
- Loewner_differential_equation wikiPageWikiLink Complex_plane.
- Loewner_differential_equation wikiPageWikiLink Conformal_field_theory.
- Loewner_differential_equation wikiPageWikiLink Conformal_map.
- Loewner_differential_equation wikiPageWikiLink Constantin_Carathéodory.
- Loewner_differential_equation wikiPageWikiLink De_Brangess_theorem.
- Loewner_differential_equation wikiPageWikiLink Disk_(mathematics).
- Loewner_differential_equation wikiPageWikiLink Geometric_function_theory.
- Loewner_differential_equation wikiPageWikiLink Holomorphic_function.
- Loewner_differential_equation wikiPageWikiLink Koebe_quarter_theorem.
- Loewner_differential_equation wikiPageWikiLink Koenigs_function.
- Loewner_differential_equation wikiPageWikiLink Louis_de_Branges_de_Bourcia.
- Loewner_differential_equation wikiPageWikiLink Mathematics.
- Loewner_differential_equation wikiPageWikiLink Oded_Schramm.
- Loewner_differential_equation wikiPageWikiLink Ordinary_differential_equation.
- Loewner_differential_equation wikiPageWikiLink Picard–Lindelöf_theorem.
- Loewner_differential_equation wikiPageWikiLink Positive_harmonic_function.
- Loewner_differential_equation wikiPageWikiLink Probability_theory.
- Loewner_differential_equation wikiPageWikiLink Riemann_mapping_theorem.
- Loewner_differential_equation wikiPageWikiLink Schramm–Loewner_evolution.
- Loewner_differential_equation wikiPageWikiLink Uniform_continuity.
- Loewner_differential_equation wikiPageWikiLink Unit_disk.
- Loewner_differential_equation wikiPageWikiLink Univalent_function.
- Loewner_differential_equation wikiPageWikiLinkText "Loewner differential equation".
- Loewner_differential_equation wikiPageWikiLinkText "Loewner equations".
- Loewner_differential_equation wikiPageUsesTemplate Template:Citation.
- Loewner_differential_equation wikiPageUsesTemplate Template:Harvtxt.
- Loewner_differential_equation wikiPageUsesTemplate Template:Reflist.
- Loewner_differential_equation subject Category:Complex_analysis.
- Loewner_differential_equation hypernym Equation.
- Loewner_differential_equation comment "In mathematics, the Loewner differential equation, or Loewner equation, is an ordinary differential equation discovered by Charles Loewner in 1923 in complex analysis and geometric function theory. Originally introduced for studying slit mappings (conformal mappings of the open disk onto the complex plane with a curve joining 0 to ∞ removed), Loewner's method was later developed in 1943 by the Russian mathematician Pavel Parfenevich Kufarev (1909–1968).".
- Loewner_differential_equation label "Loewner differential equation".
- Loewner_differential_equation sameAs Q6666620.
- Loewner_differential_equation sameAs レヴナー微分方程式.
- Loewner_differential_equation sameAs m.0hrgxzx.
- Loewner_differential_equation sameAs Q6666620.
- Loewner_differential_equation wasDerivedFrom Loewner_differential_equation?oldid=637103466.
- Loewner_differential_equation isPrimaryTopicOf Loewner_differential_equation.