# The Löwner-Kufarev representations for domains with analytic boundaries

Annales UMCS, Mathematica (2011)

- Volume: 65, Issue: 2, page 139-148
- ISSN: 2083-7402

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topDmitri Prokhorov. "The Löwner-Kufarev representations for domains with analytic boundaries." Annales UMCS, Mathematica 65.2 (2011): 139-148. <http://eudml.org/doc/268335>.

@article{DmitriProkhorov2011,

abstract = {We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions.},

author = {Dmitri Prokhorov},

journal = {Annales UMCS, Mathematica},

keywords = {Löwner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions; univalent function; Loewner chain; subordination chain; parametric method; holomorphic extension; analytic extension; bounded univalent function},

language = {eng},

number = {2},

pages = {139-148},

title = {The Löwner-Kufarev representations for domains with analytic boundaries},

url = {http://eudml.org/doc/268335},

volume = {65},

year = {2011},

}

TY - JOUR

AU - Dmitri Prokhorov

TI - The Löwner-Kufarev representations for domains with analytic boundaries

JO - Annales UMCS, Mathematica

PY - 2011

VL - 65

IS - 2

SP - 139

EP - 148

AB - We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions.

LA - eng

KW - Löwner-Kufarev equation; analytic continuation; univalent polynomials; bounded univalent functions; univalent function; Loewner chain; subordination chain; parametric method; holomorphic extension; analytic extension; bounded univalent function

UR - http://eudml.org/doc/268335

ER -

## References

top- Kufarev, P. P., On one-parametric families of analytic functions, Mat. Sbornik N. S. 13(55) (1943), 87-118 (Russian).
- Löwner, K., Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I, Math. Ann. 89 (1923), no. 1-2, 103-121. Zbl49.0714.01
- Markina, I., Vasil'ev, A., Virasoro algebra and dynamics in the space of univalent functions, Contemp. Math. 525 (2010), 85-116. Zbl1234.81127
- Pommerenke, Ch., Über die Subordination analytischer Funktionen, J. Reine Angew. Math. 218 (1965), 159-173. Zbl0184.30601
- Pommerenke, Ch., Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
- Roth, O., Schippers, E., The Loewner and Hadamard variations, Illinois J. Math. 52 (2008), no. 4, 1399-1415. Zbl1187.30005

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