scholarly journals Chordal Komatu–Loewner equation for a family of continuously growing hulls

2019 ◽  
Vol 129 (8) ◽  
pp. 2968-2990 ◽  
Author(s):  
Takuya Murayama
Keyword(s):  
Loewner Equation

scholarly journals A Komatu–Loewner Equation for Multiple Slits

2014 ◽  
Vol 14 (4) ◽  
pp. 639-663 ◽  
Author(s):  
Christoph Böhm ◽  
Wolfgang Lauf
Keyword(s):  
Loewner Equation

scholarly journals Evolution families and the Loewner equation I: the unit disc

2012 ◽  
Vol 2012 (672) ◽  
pp. 1-37 ◽  
Author(s):  
Bracci Filippo ◽  
Manuel D. Contreras ◽  
Santiago Díaz-Madrigal
Keyword(s):  
Unit Disc ◽  
Loewner Equation ◽  
Evolution Families

scholarly journals Pontryagin’s Maximum Principle for the Loewner Equation in Higher Dimensions

2015 ◽  
Vol 67 (4) ◽  
pp. 942-960 ◽  
Author(s):  
Oliver Roth
Keyword(s):  
Maximum Principle ◽  
Optimal Control Theory ◽  
Necessary Conditions ◽  
Higher Dimensions ◽  
Pontryagin’S Maximum Principle ◽  
Extremal Problems ◽  
Pontryagin's Maximum Principle ◽  
Loewner Equation ◽  
First Order ◽  
The Pontryagin Maximum Principle

AbstractIn this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin’s maximum principle from optimal control theory for the Loewner equation in several complex variables. Based on recent work of Arosio, Bracci, and Wold, we then apply our version of the Pontryagin maximum principle to obtain first-order necessary conditions for the extremal mappings for a wide class of extremal problems over the set of normalized biholomorphic mappings on the unit ball in ℂn.

scholarly journals The chordal Loewner equation and monotone probability theory

2017 ◽  
Vol 20 (03) ◽  
pp. 1750016 ◽  
Author(s):  
Sebastian Schleißinger
Keyword(s):  
Probability Theory ◽  
Evolution Equations ◽  
Free Probability ◽  
Noncommutative Probability ◽  
Loewner Equation ◽  
Free Probability Theory ◽  
Chordal Loewner Equation ◽  
Monotone Probability ◽  
Noncommutative Probability Theory

In Ref. 5, O. Bauer interpreted the chordal Loewner equation in terms of noncommutative probability theory. We follow this perspective and identify the chordal Loewner equations as the non-autonomous versions of evolution equations for semigroups in monotone and anti-monotone probability theory. We also look at the corresponding equation for free probability theory.

Driving functions and traces of the Loewner equation

2013 ◽  
Vol 57 (8) ◽  
pp. 1615-1624 ◽  
Author(s):  
HaiHua Wu ◽  
XinHan Dong
Keyword(s):  
Loewner Equation

scholarly journals Spacefilling curves and phases of the Loewner equation

2012 ◽  
Vol 61 (6) ◽  
pp. 2231-2249 ◽  
Author(s):  
Joan Lind ◽  
Steffen Rohde
Keyword(s):  
Loewner Equation
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