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

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 . 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 as . [ABSTRACT FROM AUTHOR]