Distortion of area and dimension under quasiconformal mappings in the plane.
Distortion of area and dimension under quasiconformal mappings in the plane.
复制标题
平面内准共形映射下面积和尺寸的畸变。
DOI：
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发表时间：
1993
影响因子：
11.1
通讯作者：
K. Astala
中科院分区：
文献类型：
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作者：
K. Astala
在复平面的K-拟共形映射下，我们得到了面积和Hausdorff维数的畸变的精确估计。这也解决了找到指数p的精确界p（K）的问题，使得对于每个平面K-拟共形映射f，雅可比矩阵Jf是局部p-可积的;它遵循p（K）= 2K/（K - 1）。进一步的后果包括除其他外的正则性和可移除性的结果拟正则映射和尖锐的估计复杂的希尔伯特变换。
We find the exact estimates for the distortion of area and Hausdorff dimension under a K-quasiconformal mapping of the complex plane. This solves also the problem of finding the precise bound p(K) of the exponents p such that for each planar K-quasiconformal mapping f the Jacobian Jf is locally p-integrable; it follows that p(K) = 2K/(K - 1). Further consequences include among others the regularity and removability results for quasiregular mappings and sharp estimates for the complex Hilbert transform.