US-Sweden Cooperative Research: Hyperbolic Geometry and Quasiconformal Mappings

该奖项将支持纽约城市大学皇后学院数学系的Ravi Kulkarni博士在瑞典斯德哥尔摩的米塔格-莱弗勒研究所工作9个月。这个在古典分析方面有着百年传统的研究所，正在举办一个特别学年，主题是“双曲几何和拟共形映射”。在这一年中，Kulkarni博士将与两位芬兰数学家，dr。赫尔辛基大学的Seppo Rickman和Pekka Tukia，他们将在研究所指导这个特别项目。里克曼博士在拟共形和更普遍的拟正则映射方面进行了开创性的工作。通过这项工作，越来越明显地表明，这种“准正则”方向是经典几何函数理论的正确推广。值得注意的是，里克曼在高维中得到了经典皮卡德定理的完整推广。最近，他还获得了更高维度的Nevanlinna-Ahlfors缺陷关系的强形式。由于他在拟共形映射的可拓性质和经典的fuchsian和kleinian群理论的几何特征方面的广泛工作，Tukia博士也享有世界声誉。在研究所期间，Kulkarni博士将重点研究以下内容：(1)黎曼曲面的模空间结构(2)fuchsian群和kleinian群及其推广的拓扑方面的研究(3)莫比乌斯结构。这项研究的结果将对理解这一几何分析领域做出重大贡献。

This award will support Dr. Ravi Kulkarni, Department of Mathematics, Queens College, City University of New York, to spend nine months at the Mittag-Leffler Institute in Stockholm, Sweden. This institute, which has a century-old tradition in classical analysis, is sponsoring a special academic year on the topic of "Hyberbolic Geometry and Quasiconformal Mappings." During this year, Dr. Kulkarni will carry out collaborative research with two Finnish mathematicians, Drs. Seppo Rickman and Pekka Tukia, University of Helsinki, who will be directing this special program at the institute. Dr. Rickman has carried out a pioneering work in quasiconformal and more generally quasiregular mappings. Through this work it has become increasingly evident that this "quasiregular" direction is a right generalization of the classical geometric function theory. Notably Rickman obtained complete generalizations of the classical Picard's theorem in higher dimensions. Recently he has also obtained strong forms of the Nevanlinna-Ahlfors defect relations in higher dimensions. Dr. Tukia also has a worldwide reputation due to his extensive work on the extension properties of quasiconformal mappings and geometric features of the classical theories of fuchsian and kleinian groups. During his stay at the institute, Dr. Kulkarni will focus on the following: (1) the structure of moduli spaces of Riemann surfaces (2) the study of topological aspects of fuchsian and kleinian groups and their generalizations (3) mobius structures. The results of this research should make a significant contribution to understanding this area of geometric analysis.