Assume that $\unicode[STIX]{x1D6FA}$ and $D$ are two domains with compact smooth boundaries in the extended complex plane $\overline{\mathbf{C}}$. We prove that every quasiconformal mapping between $\unicode[STIX]{x1D6FA}$ and $D$ mapping $\infty$ onto itself is bi-Lipschitz continuous with respect to both the Euclidean and Riemannian metrics.

中文翻译：

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包含无穷大的域之间的准共形谐波映射

假使，假设$\unicode[STIX]{x1D6FA}$和$D$是扩展复平面上具有紧致平滑边界的两个域$\overline{\mathbf{C}}$. 我们证明了每个之间的准共形映射$\unicode[STIX]{x1D6FA}$和$D$映射$\infty$就欧几里得和黎曼度量而言，它本身是双李普希茨连续的。