Area distortion under certain classes of quasiconformal mappings
نویسندگان
چکیده
In this paper we study the hyperbolic and Euclidean area distortion of measurable sets under some classes of K-quasiconformal mappings from the upper half-plane and the unit disk onto themselves, respectively.
منابع مشابه
Sharp Examples for Planar Quasiconformal Distortion of Hausdorff Measures and Removability
In the celebrated paper [Ast94], Astala showed optimal area distortion bounds and dimension distortion estimates for planar quasiconformal mappings. He asked (Question 4.4) whether a finer result held, namely absolute continuity of Hausdorff measures under push-forward by quasiconformal mappings. This was proved in one particular case relevant for removability questions, in joint work of Astala...
متن کامل2000]Primary 30C80 DISTORTION IN THE SPHERICAL METRIC UNDER QUASICONFORMAL MAPPINGS
This paper contains bounds for the distortion in the spherical metric, that is to say bounds for the constant of Hölder continuity of mappings f : (R, q) → (R, q) where q denotes the spherical metric. The mappings considered are K-quasiconformal (K ≥ 1) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as K → 1.
متن کاملDistortion in the Spherical Metric under Quasiconformal Mappings
This paper contains bounds for the distortion in the spherical metric, that is to say, bounds for the constant of Hölder continuity of mappings f : (Rn, q) → (Rn, q) where q denotes the spherical metric. The mappings considered are K-quasiconformal (K ≥ 1) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as K → 1.
متن کاملThe Distortion Theorem for Quasiconformal Mappings, Schottky’s Theorem and Holomorphic Motions
We prove the equivalence of Schottky’s theorem and the distortion theorem for planar quasiconformal mappings via the theory of holomorphic motions. The ideas lead to new methods in the study of distortion theorems for quasiconformal mappings and a new proof of Teichmüller’s distortion theorem.
متن کاملOn the Area Distortion by Quasiconformal Mappings
We give the sharp constants in the area distortion inequality for quasiconformal mappings in the plane. Astala [1] proved the following theorem conjectured by Gehring and Reich in [3]: Theorem A. Let f be a K-quasiconformal mapping of D = {z: \z\ < 1} onto itself with f(0) = 0. Then for any measurable E c D we have \f(E)\<C(K)\E\xlK, where \ • \ stands for the area. The first author [2] obtaine...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
دوره 2017 شماره
صفحات -
تاریخ انتشار 2017