Mathematical Sciences: Topics in Geometric Function Theory

数学科学：几何函数论专题

• 批准号: 9401504
• 负责人: C. David Minda
• 金额: $ 5万
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401504&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Geometric; Function

9401504 Minda This award supports a continuing program of mathematical research applying differential geometric methods to a variety of problems in complex function theory. The common thread joining the parts of the investigation is the use of conformal geometries, especially the three classical geometries: hyperbolic, euclidean and spherical. Comparison results will be sought, that is, relating quantities in one conformal geometry to like quantities in another. Work will also be done analyzing holomorphic functions viewed as mappings from on geometry to another. For example, Bloch functions are precisely those holomorphic functions from hyperbolic to euclidean geometry which have bounded distortion. Ongoing research is also focusing on two-point comparisons for conformal geometries. This will directly apply to the understanding of two-point distortions for univalent functions. Finally, work will be done using subordination principles as the basis for a systematic study of Bloch functions. This approach has yet to be employed seriously. This project represents research at the boundary of differential geometry and classical complex function theory. The tools available are considerable, in the hands of investigators who have mastered the techniques of both areas. ***

小行星9401504 该奖项支持一个持续的数学研究计划，将微分几何方法应用于复变函数理论中的各种问题。 共同的线程连接部分的调查是使用共形几何，特别是三个经典的几何：双曲，欧几里德和球面。 将寻求比较结果，即，将一个共形几何中的量与另一个共形几何中的类似量相关联。 工作也将完成分析全纯函数视为从一个几何映射到另一个。 例如，布洛赫函数正是那些从双曲几何到欧几里得几何的全纯函数，它们具有有界失真。 正在进行的研究也集中在两点比较共形几何。 这将直接应用于理解单叶函数的两点畸变。 最后，工作将使用从属原则的基础上进行系统的研究布洛赫函数。 这一办法尚未得到认真采用。 这个项目代表了微分几何和经典复变函数理论的边界研究。 掌握这两个领域技术的调查人员手中有大量的工具。 ***