Geodesic
Integrability of a partial case of the Lëwner equation
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 19-23 
D. V. Prokhorov; A. M. Zaharov. Integrability of a partial case of the Lëwner 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/
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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.

[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