Value range of solutions to the chordal Loewner equation with restriction on the driving function
Problemy analiza, Tome 8 (2019) no. 2, pp. 92-104.

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We consider a value range $\{g(i, T)\}$ of solutions to the chordal Loewner equation with the restriction $|\lambda(t)| \le c$ on the driving function. We use reachable set methods and the Pontryagin maximum principle.
Keywords: Value range, Loewner equation, Hamilton function, Pontryagin maximum principle.
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A. V. Zherdev. Value range of solutions to the chordal Loewner equation with restriction on the driving function. Problemy analiza, Tome 8 (2019) no. 2, pp. 92-104. http://geodesic.mathdoc.fr/item/PA_2019_8_2_a6/

[1] Goryainov V. V., Gutlyanski V. Ja., “On extremal problems in the class $S_M$”, Mat. Sb., Kiev, 1976, 242–246 | MR

[2] Grunsky H., “Neue Abschätzungen zur konformen Abbildung ein- und mehrfach zusammenhängender Bereiche”, Schr. Math. Sem. Inst. Angew. Math. Univ. Berl., 1 (1932), 93–140

[3] Kager W., Nienhuis B., Kadanoff L. P., “Exact Solutions for Loewner Evolutions”, J. Stat. Phys., 115 (2004), 805–822 | DOI | MR | Zbl

[4] Koch J., Schleissinger S., “Value ranges of univalent self-mappings of the unit disc”, J. Math. Anal. Appl., 433:2 (2016), 1772–1789 | DOI | MR | Zbl

[5] Koch J., Schleissinger S., “Three value ranges for symmetric self-mappings of the unit disc”, Proc. Amer. Math. Soc., 145 (2017), 1747–1761 | DOI | MR | Zbl

[6] Math. USSR Sb., 71:2 (1992), 499–516 | DOI | MR | Zbl | Zbl

[7] Prokhorov D. V., Reachable Set Methods in Extremal Problems for Univalent Functions, Saratov Univ., Saratov, 1993 | MR | Zbl

[8] Prokhorov D. V., Samsonova K., “Value range of solutions to the chordal Loewner equation”, J. Math. Anal. Appl., 428:2 (2015), 910–919 | DOI | MR | Zbl

[9] Rogosinski W., “Zum Schwarzen Lemma”, Jahresber. Dtsch. Math.-Ver., 44 (1934), 258–261

[10] Roth O., Schleissinger S., “Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation”, Bull. Lond. Math. Soc., 46:5 (2014), 1099–1109 | DOI | MR | Zbl