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Asymptotics of the exterior conformal modulus of a symmetric quadrilateral under stretching map

A. DyutinGiang V. Nguyen
Dec 2022
摘要
In this work, we study the distortion of the exterior conformal modulus of asymmetric quadrilateral, when stretched in the direction of the abscissa axiswith the coefficient $H\to \infty$. By using some facts from the theory ofelliptic integrals, we confirm that the asymptotic behavior of this modulusdoes not depend on the shape of the boundary of the quadrilateral; moreover, itis equivalent to $(1/\pi)\log H$ as $H\to \infty$.
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