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Characterization of Quasiconformal M...

Zou, Wenfei.

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Characterization of Quasiconformal Mappings and Extremal Length Decomposition.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Characterization of Quasiconformal Mappings and Extremal Length Decomposition./
作者:	Zou, Wenfei.
面頁冊數:	78 p.
附註:	Source: Dissertation Abstracts International, Volume: 75-11(E), Section: B.
Contained By:	Dissertation Abstracts International75-11B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3634431
ISBN:	9781321150032

Characterization of Quasiconformal Mappings and Extremal Length Decomposition.
Zou, Wenfei.

Characterization of Quasiconformal Mappings and Extremal Length Decomposition. - 78 p.

Source: Dissertation Abstracts International, Volume: 75-11(E), Section: B.

Thesis (Ph.D.)--Emory University, 2014.

Quasiconformal mappings have abundant subtle analytic and geometric properties, which can be used widely in various contexts. The reason probably lies in that there exists several equivalent definitions for quasiconformal mappings. While conformal mappings preserve measures of angles, quasiconformal mappings are their natural generalizations. Geometrically, a quasiconformal mapping maps infinitesimal balls to infinitesimal ellipsoids with uniformly controlled eccentricity in space. This suggests that it is reasonable to use measures of angles to characterize quasiconformal mappings. In the first part of this dissertation, a measure of angle called topological angle is used to characterize quasiconformal mappings in higher dimensional Euclidean space, generalizing a similar result in the plane.

ISBN: 9781321150032Subjects--Topical Terms:

515831
Mathematics.

Characterization of Quasiconformal Mappings and Extremal Length Decomposition.
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500 $a Adviser: Shanshuang Yang.
502 $a Thesis (Ph.D.)--Emory University, 2014.
520 $a Quasiconformal mappings have abundant subtle analytic and geometric properties, which can be used widely in various contexts. The reason probably lies in that there exists several equivalent definitions for quasiconformal mappings. While conformal mappings preserve measures of angles, quasiconformal mappings are their natural generalizations. Geometrically, a quasiconformal mapping maps infinitesimal balls to infinitesimal ellipsoids with uniformly controlled eccentricity in space. This suggests that it is reasonable to use measures of angles to characterize quasiconformal mappings. In the first part of this dissertation, a measure of angle called topological angle is used to characterize quasiconformal mappings in higher dimensional Euclidean space, generalizing a similar result in the plane.
520 $a The second part of the dissertation deals with some important conformal invariants in the study of geometric function theory, such as quasiextremal distance (or QED) constant and extremal length. QED domains are a class of domains closely connected to quasiconformal mapping theory. The QED constant is a naturally defined conformal invariant on a domain whose values reflect the geometry of a domain. In this part, a sharp upper bound for the QED constant in terms of boundary dilatation is obtained for a finitely connected domain on the complex plane. Furthermore, the extremal length (or its reciprocal called modulus) of a curve family plays an essential role in studying quasiconformal mappings. In the second part of this dissertation, a decomposition result is established for the extremal length of a curve family in a finitely connected domain. This can be regarded as a natural generalization of subadditivity of extremal length. It is also a key ingredient in obtaining the sharp upper bound for the QED constant mentioned above.
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