Asymptotics of the Exterior Conformal Modulus of a Symmetric Quadrilateral under Stretching Map

被引：1

作者：

Dyutin, A. ^{[1
]}

Nguyen, Giang V. ^{[1
]}

机构：

[1] Kazan Fed Univ, Kazan 420008, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 04期

关键词：

quadrilateral; conformal modulus; exterior conformal modulus; quasiconformal mapping; convergence of domains to a kernel; DOUBLY CONNECTED DOMAIN;

D O I：

10.1134/S1995080223040078

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we study the distortion of the exterior conformal modulus of a symmetric quadrilateral, when stretched in the direction of the abscissa axis with the coefficient H ->infinity. By using some facts from the theory of elliptic integrals, we confirm that the asymptotic behavior of this modulus does not depend on the shape of the boundary of the quadrilateral; moreover, it is equivalent to (1/pi) logH as H ->infinity.

引用

页码：1289 / 1298

页数：10

共 18 条

[1]

Ahlfors L.V., 2006, Lectures on quasiconformal mappings, V38

[2]

Anderson GD., 1997, Conformal invariants, inequalities, and quasiconformal maps

[3]

Bickley WG, 1934, P LOND MATH SOC, V37, P82

[4]

Byrd P. F., 1971, Handbook of Elliptic Integrals for Engineers and Sciensists

[5] Asymptotics of Conformal Module of Nonsymmetric Doubly Connected Domain under Unbounded Stretching Along the Real Axis [J].

Dautova, D. ;

Nasyrov, S. .

LOBACHEVSKII JOURNAL OF MATHEMATICS, 2019, 40 (09) :1268-1274

[6] Asymptotics of the Modules of Mirror Symmetric Doubly Connected Domains under Stretching [J].

Dautova, D. N. ;

Nasyrov, S. R. .

MATHEMATICAL NOTES, 2018, 103 (3-4) :537-549

[7]

Dubinin V., 2014, Condenser capacities and symmetrization in geometric function theory, DOI [10.1007/978-3-0348-0843-9, DOI 10.1007/978-3-0348-0843-9]

[8] ROBIN CAPACITY AND EXTREMAL LENGTH [J].

DUREN, P ;

PFALTZGRAFF, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 179 (01) :110-119

[9]

Goluzin G.M., 1969, Geometric Theory of Functions of a Complex Variable, V26

[10]

Hakula H, 2013, ELECTRON T NUMER ANA, V40, P436

← 1 2 →