The Exceptional Sets for the Differentiability of Plane Quasiconformal Mappings
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Date
1989-06-??
Authors
黃文達
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Publisher
國立臺灣師範大學研究發展處
Office of Research and Development
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.
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.