Geodesic
Nonlinear Beltrami equation: lower estimates of Schwarz lemma’s type
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 533-543

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DOI

We study a nonlinear Beltrami equation $f_\theta =\sigma \,|f_r|^m f_r$ in polar coordinates $(r,\theta ),$ which becomes the classical Cauchy–Riemann system under $m=0$ and $\sigma =ir.$ Using the isoperimetric technique, various lower estimates for $|f(z)|/|z|, f(0)=0,$ as $z\to 0,$ are derived under appropriate integral conditions on complex/directional dilatations. The sharpness of the above bounds is illustrated by several examples.
DOI : 10.4153/S0008439523000942
Mots-clés : Beltrami equation, nonlinear Beltrami equation, nonlinear Cauchy–Riemann system, asymptotic behavior, Schwarz lemma 
Petkov, Igor; Salimov, Ruslan; Stefanchuk, Mariia. Nonlinear Beltrami equation: lower estimates of Schwarz lemma’s type. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 533-543. doi: 10.4153/S0008439523000942
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     title = {Nonlinear {Beltrami} equation: lower estimates of {Schwarz} lemma{\textquoteright}s type},
     journal = {Canadian mathematical bulletin},
     pages = {533--543},
     year = {2024},
     volume = {67},
     number = {3},
     doi = {10.4153/S0008439523000942},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000942/}
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