报告人：黄志波教授

报告时间：2025年11月21日 下午4:00

报告地点：数学系715

报告摘要：This paper studies the harmonic integral operator$f_{\lambda_{1}, \alpha}=h_{\alpha}(z)+\lambda_{1}\overline{[(h+g)_{\alpha}(z)-h_{\alpha}(z)]}$ in the unit disk $\mathbb{D}$, where $\alpha$ and $\lambda_{1}$ are complex parameters satisfying $|\alpha|\leq 1$ and $|\lambda_{1}|\leq 1$.  We establish sharp univalence criteria, explicit quasiconformal extension formula and quasi-circle characterization for this operator. Key results include: (1) an improved univalence bound for $\alpha$, partly resolving the critical range $1/4<\alpha\leq 1/3$ for harmonic mappings; (2) the explicit $K-$quasiconformal extension to $\mathbb{C}$ with a computable dilatation $K$; and (3) a continuous extension $\widetilde{f_{\lambda_{1},\alpha}}$ satisfying that $\widetilde{f_{\lambda_{1},\alpha}}(\partial \mathbb{D})$ is a quasicircle. Some concrete examples demonstrate the sharpness and applicability of the criteria.

报告人简介：黄志波，教授，华南师范大学教学名师，华南师范大学数学科学学院数学与应用数学系主任。主要研究兴趣：复域微分方程与差分方程及其动力学性质，拟共形映射。主持和参与国家自然科学基金8项，广东省自然科学基金4项。主持拔尖人才培养省级质量工程、国家一流本科课程、广东省一流本科课程、广东省在线开放课程和广东省精品资源共享课程。

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