Geodesic
Integrability of a~partial case of the L\"ewner equation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 19-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

We give a quadrature solution to the partial case of the Lëwner equation for the upper half-plane. 
@article{ISU_2010_10_2_a2,
     author = {D. V. Prokhorov and A. M. Zaharov},
     title = {Integrability of a~partial case of the {L\"ewner} equation},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {19--23},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a2/}
}
TY  - JOUR
AU  - D. V. Prokhorov
AU  - A. M. Zaharov
TI  - Integrability of a~partial case of the L\"ewner equation
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2010
SP  - 19
EP  - 23
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a2/
LA  - ru
ID  - ISU_2010_10_2_a2
ER  - 
%0 Journal Article
%A D. V. Prokhorov
%A A. M. Zaharov
%T Integrability of a~partial case of the L\"ewner equation
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2010
%P 19-23
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a2/
%G ru
%F ISU_2010_10_2_a2
D. V. Prokhorov; A. M. Zaharov. Integrability of a~partial case of the L\"ewner equation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 19-23. http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a2/

[1] K. Löwner, “Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I”, Math. Ann., 89:1–2 (1923), 103–121 | DOI | MR | Zbl

[2] I. A. Aleksandrov, Parametricheskie prodolzheniya v teorii odnolistnykh funktsii, Nauka, M., 1976 | MR

[3] W. Kager, B. Nienhuis, L. P. Kadanoff, “Exact solutions for Loewner evolutions”, J. Statist. Phys., 115:3–4 (2004), 805–822 | DOI | MR | Zbl

[4] P. P. Kufarev, “Odno zamechanie ob uravnenii Levnera”, Dokl. AN SSSR, 57 (1947), 751–754 | MR | Zbl

[5] D. Marshall, S. Rohde, “The Löwner differential equation and slit mappings”, J. Amer. Math. Soc., 18:4 (2005), 763–778 | DOI | MR | Zbl

[6] J. Lind, “A sharp condition for the Löwner equation to generate slits”, Ann. Acad. Sci. Fenn. Math., 30:1 (2005), 143–158 | MR | Zbl

[7] D. Prokhorov, A. Vasil'ev, “Singular and tangent slit solutions to the Löwner equation”, Analysis and Mathematical Physics, Trends in Mathematics, eds. B. Gustafsson, A. Vasil'ev, Birkhauser, Basel, 2009, 451–459 | MR