US-Sweden Cooperative Research: Hyperbolic Geometry and Quasiconformal Mappings

美国-瑞典合作研究：双曲几何和拟共形映射

• 批准号: 8912515
• 负责人: Ravi Kulkarni
• 金额: $ 2万
• 依托单位: CUNY Queens College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-10-15 至 1991-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8912515&HistoricalAwards=false
• 关键词: US; Sweden; Cooperative; Research; Hyperbolic

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.

该奖项将支持纽约市皇后学院数学系Ravi Kulkarni博士在瑞典斯德哥尔摩的Mittag-Leffler研究所度过9个月。 该研究所在古典分析中具有百年历史的传统，它赞助了一个关于“水晶几何和准文化映射”主题的特殊学年。 在今年，Kulkarni博士将与两位芬兰数学家Drs进行合作研究。 Seppo Rickman和Pekka Tukia，赫尔辛基大学，他们将在该研究所指导这一特别计划。 里克曼博士在准信息和更通常的准映射映射方面开展了开创性的工作。 通过这项工作，越来越明显的是，这个“ Quasiregular”方向是对经典几何函数理论的正确概括。 尤其是里克曼（Rickman）在更高维度上获得了古典Picard定理的完全概括。 最近，他还获得了较高维度的Nevanlinna-Ahlfors缺陷关系的强烈形式。 Tukia博士在全球范围内的声誉也享有广泛的作品，该作品在紫红色和克莱尼亚群体的古典映射的扩展特性以及几何特征。 在该研究所逗留期间，Kulkarni博士将重点关注以下内容：（1）Riemann表面的模量空间的结构（2）研究Fuchsian和Kleinian群体及其概括（3）Mobius结构的拓扑方面的研究。 这项研究的结果应为理解几何分析的这一领域做出重要贡献。