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Title: The Exceptional Sets for the Differentiability of Plane Quasiconformal Mappings
Other Titles: 平面擬保角變換可微分性的例外集
Authors: 黃文達
Issue Date: Jun-1989
Publisher: 國立臺灣師範大學研究發展處
Office of Research and Development
Abstract: 我們主要探討平面上一個擬保角變換的可微分性,首先證明一個K-擬保角變換f幾乎到處可微分。接著討論它的不可微分集X(f),當k=1時,它是空集合;但當k>1時,它可達到最大可能,其Hausdorff維度可為2。
We investigate the differentiability of plane quasiconformal mappings and prove that a K-quasiconformal mapping f is differentiable almost everywhere. The ex-ceptional set X(f) for the differentiability is empty if K=l, and it can be enlarged to Hausdorff dimension 2 if K>1.
Other Identifiers: C863B21E-7F51-F845-48A8-7B1D8B283A58
Appears in Collections:師大學報

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