通过准共形映射的平面椭圆度量的豪斯多夫维度

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-07-30 DOI:arxiv-2407.21145

Ignasi Guillén-Mola

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摘要

在本文中，我们通过应用准共形映射来研究平面椭圆度量的维数。事实上，在我们的案例研究中，我们找到了将某域中的椭圆度量与其像域中的谐波度量联系起来的准共形映射，并通过谐波侧的已知结果推导出了椭圆度量的豪斯多夫维度边界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Hausdorff dimension of planar elliptic measures via quasiconformal mappings

In this paper we study the dimension of planar elliptic measures via the application of quasiconformal mappings. In fact, in our case studies, we find a quasiconformal mapping that relates the elliptic measure in a domain to the harmonic measure in its image domain, and we deduce bounds for the Hausdorff dimension of the elliptic measure by the known results on the harmonic side.

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arXiv - MATH - Classical Analysis and ODEs

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