Beltrami equations in Clifford analysis
Prof. Uwe Kaehler, CIDMA e Departamento de Matematica, Universidade de Aveiro, PORTUGAL.
研究生教育创新计划高水平学术前沿讲座【Prof. Uwe Kaehler】 时间：2013年4月25日（星期五）下午4：00-5：00 地点：管理科研楼1518 摘要：Beltrami equations play an important role in complex analysis due to the fact that its solutions are quasi-conformal mappings. Although there is a well-developed theory of quasi-conformal mappings in higher dimensions, particularly in the framework of so-called quasi-regular mappings, the same cannot be said about the theory of Beltrami equations in the framework of Quaternionic and Clifford analysis, although its history goes back to the works of Shevchenko in the 1960's. This is due to the additional difficulties which can be experienced in higher dimension. For instance, while in complex analysis one of the definitions of a quasi-conformal mapping is to be a solution of a Beltrami equation the same cannot be stated so clearly in higher dimensions. Nevertheless, the study of Beltrami equations in higher dimensions is not only interesting from the point of view of its connections with quasi-conformality, but also because of its links with other important topics such as the study of Dirac operators with non-constant coefficients. In this talk we discuss the solvability of quaternionic and Clifford-Beltrami equations and present some properties of their solutions, in cases were they exist, such as local and global quasi-conformality. We also discuss connections of the theory of Beltrami equations with other areas. 主办单位：中国科学技术大学研究生院、中国科学技术大学数学学院