Long and Medium-Term Research: Investigation of Quasicon- formal Equivalence Classes of Spherical CR Manifolds

中长期研究：球形CR流形拟共形等价类的研究

• 批准号: 9102437
• 负责人: Robert Miner
• 金额: --
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1991-12-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102437&HistoricalAwards=false
• 关键词: Long; Medium; Term; Research; Investigation

Long & Medium-Term Research: Investigation of Quasicon- formal Equivalence Classes of Spherical CR Manifolds This award is made under the Program for Long- & Medium- Term Research at Foreign Centers of Excellence, which enables U.S. postdoctoral researchers to conduct 3 to 12 months' joint research abroad at centers of proven excellence, allowing them access to unique or complementary facilities, expertise and experimental conditions in other countries. This award will support a 12-month visit by Dr. Robert Miner of the University of Maryland, College Park, with Professor H.M. Reimann, Universit>t Bern, Switzerland. Dr. Miner will investigate quasiconformal equivalence classes of spherical CR manifolds based on his earlier classification of CR manifolds with amenable holonomy. Up to finite cover, such a manifold is either S.n-1, a nilmanifold, or the Heisenberg analog of a Hopf manifold, a manifold homeomorphic to S1 X S.n. There is a natural notion of a quasiconformal homeomorphism between manifolds with CR structures, which he hopes to refine up to quasiconformal equivalence. In his dissertation, Dr. Miner showed homeomorphic nilmanifolds arising as covers of spherical CR manifolds with amenable holonomy are actually quasiconformal. In dimension three, the mappings can be explicitly described. With Heisenberg Hopf manifolds, the question is more difficult. Dr. Miner will explore techniques for analyzing this case, and for investigating related questions about quasiconformal equivalence of domains of the Heisenberg group. Eliashberg has described invariants of the symplectic manifold canonically associated to a CR manifold and has shown that certain tori are not quasiconformally equivalent, and these invariants may be more widely applicable. Given a pair of domains, one can define an associated pseudoconformal capacity, which transforms nicely under quasiconformal mappings. From this, Reimann, Pansu, and others have been able to deduce global distortion properties which may be useful in analyzing quasiconformal equivalence. Kor>nyi and Reimann have developed a theory of deformations of quasiconformal mappings on the Heisenberg group. In some cases Goldman and Miner have produced quasiconformal mappings by applying this theory, and there is hope it can be extended to a wider class of examples. The award provides funds for international travel and a flat administrative allowance of $250 for his home institution.

长期中期研究：准晶体的研究 球面CR流形的形式等价类 该奖项是根据长期-中等- 在国外卓越中心的长期研究， 使美国博士后研究人员能够进行3至12 几个月的联合研究在国外的中心， 卓越，使他们能够获得独特的或互补的 设施、专门知识和实验条件 其他国家 该奖项将支持罗伯特博士为期12个月的访问 马里兰州大学帕克分校的迈纳， H.M.教授Reimann，Universit>t伯尔尼，瑞士. Miner博士将研究拟共形等价 类的球面CR流形的基础上，他的早期 具有顺从完整性的CR流形的分类。 直到有限覆盖，这样的流形或者是S.n-1， nilmanifold，或Heisenberg类似的Hopf流形， 同胚于S1 X S.n.的流形 有一种自然 流形间拟共形同胚的概念 与CR结构，他希望完善， 拟共形等价 在他的论文中，博士。 Miner证明了同胚的nilmanifold作为覆盖而产生 的球面CR流形与顺从holonomy是 实际上是拟共形的 在三维空间中， 可以显式描述映射。 和海森伯 Hopf流形，这个问题比较难。 迈纳博士 将探索分析这种情况的技术， 拟共形的相关问题研究 海森堡群的域的等价性 Eliashberg 描述了辛流形的不变量 正则地关联到CR流形，并且已经表明， 某些环面不是拟共形等价的，这些环面 不变量可以更广泛地应用。 给定一对 域，可以定义相关的伪共形 容量，在拟共形下很好地转换 映射。 从这一点上，雷曼，潘苏，和其他人已经被 能够推断出全局失真特性， 在分析拟共形等价时很有用。 Kor>nyi 和Reimann发展了一种变形理论， Heisenberg群上的拟共形映射 在一些 高盛和迈纳提出的拟共形问题 映射通过应用这个理论，有希望， 可以扩展到更广泛的例子。 该奖项为国际旅行提供资金， 250美元的家庭行政津贴 机构。