Area distortion under quasiconformal mappings
نویسندگان
چکیده
منابع مشابه
Area distortion under certain classes of quasiconformal mappings
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.
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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...
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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.
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© Bulletin de la S. M. F., 1986, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impress...
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Teichmüller’s classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given point of the domain to another given point of the domain. For a domain D ⊂ Rn , n ≥ 2 , we consider the class of all Kquasiconformal maps of D onto itself with...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Series A I Mathematica
سال: 1966
ISSN: 0066-1953
DOI: 10.5186/aasfm.1966.388