US-Sweden Cooperative Research: Hyperbolic Geometry and Quasiconformal Mappings

该奖项将支持拉维Kulkarni博士，数学系， 纽约皇后学院， 在瑞典斯德哥尔摩的米塔格-莱弗勒研究所。 这 该研究所在古典分析方面有着百年传统， 正在赞助一个特别的学年，主题是“混合动力”， 几何与拟共形映射。”在这一年里，博士。 Kulkarni将与两名芬兰人进行合作研究。 数学家，塞波·里克曼和佩卡·图基亚博士， 赫尔辛基，谁将指导这个特别节目在 院 瑞克曼博士进行了一项开创性的工作， 拟共形映射和更一般的拟正则映射。 通过 这项工作已经变得越来越明显，这种“准正规” 方向是经典几何的右推广 功能理论 值得注意的是里克曼得到了完整的概括 经典的皮卡德定理在更高维度的应用。 最近 他还得到了Nevanlinna-Ahlfors缺陷的强形式 更高维度的关系。 Tukia博士还拥有一个全球性的 由于他在扩展属性方面的广泛工作， 拟共形映射及其几何特征 Fuchsian和Kleinian群理论 在研究所逗留期间，Kulkarni博士将重点研究 （1）Riemann曲面模空间的结构 (2)fuchsian和kleinian的拓扑学研究 群及其推广（3）Mobius结构。 的 这项研究的结果应该做出重大贡献 理解这一领域的几何分析。

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.