Rigidity in negative curvature and quasiconformal analysis
负曲率刚性和拟共形分析
基本信息
- 批准号:1105500
- 负责人:
- 金额:$ 6.26万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-07-01 至 2012-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The PI proposes to investigate the large scale geometry of negatively curved spaces by using quasiconformal analysis on metric spaces. The proposed research includes large scale geometry of solvable groups, metric structure on the boundary of relatively hyperbolic groups, and quasiisometric rigidity of Hadamard manifolds. The proposed research on solvable groups involves the study of quasiconformal analysis on nilpotent Lie groups. Although the metrics on the nilpotent Lie groups are not Riemannian, they are left invariant and admit a one-parameter family of dilations. They include Carnot metrics and also many other metrics. Stated in the language of quasiconformal analysis, some of the goals are: to classify these nilpotent Lie groups up to quasiconformal equivalence; to show that (in most cases) every quasiconformal map is biLipschitz. In terms of large scale geometry, the goal is to show that quasiisometries between (most) negatively curved solvable Lie groups preserve distance up to an additive constant and sometimes are even at a finite distance from isometries. If successful, this research will lead to progress on the large scale geometry of finitely generated solvable groups. The proposed research on relatively hyperbolic groups will try to determine if there is a canonical quasiconformal structure on the boundary of relatively hyperbolic groups. % and the limit sets of geometrically finite groups. It would have applications to rigidity questions about these groups. The proposed research about Hadamard manifolds concerns the question whether every quasiisometry between Hadamard manifolds is at a finite distance from a biLipschitz homeomorphism. The proposed projects on negatively curved solvable Lie groups and Hadamard manifolds are continuation of the PI's previous work on these topics. A common theme of these proposed projects is the interplay between geometry of negatively curved spaces and analysis on the ideal boundary of these spaces.The proposed research lies in geometric group theory and geometric analysis. The questions in geometric group theory often concern the large scale properties of the spaces or maps, while in analysis the main focus is often the local properties. Surprisingly, these are related for spaces with negative curvature: a negatively curved space has an ideal boundary, and the large scale properties of the spaces are encoded in the local structure of the ideal boundary. The PI proposes to study the large scale properties of negatively curved spaces by investigating the ideal boundary using geometric analysis.
PI提出利用度量空间上的拟共形分析来研究负曲空间的大规模几何问题。研究内容包括可解群的大规模几何、相对双曲群边界上的度量结构以及Hadamard流形的拟等距刚性。关于可解群的研究涉及幂零李群上的拟共形分析。虽然幂零李群上的度量不是黎曼度量,但它们是不变的,并且允许一个参数伸缩族。它们包括卡诺指标和许多其他指标。用拟共形分析的语言表述,其中一些目标是:将这些幂零李群分类到拟共形等价;证明(在大多数情况下)每个拟共形映射都是双Lipschitz映射。在大尺度几何方面,我们的目标是证明(大多数)负曲线可解李群之间的拟等距保持最大可加常数的距离,有时甚至与等距保持有限距离。如果这一研究取得成功,将推动有限生成可解群的大规模几何研究的进展。关于相对双曲群的拟议研究将试图确定在相对双曲群的边界上是否存在规范的拟共形结构。%和几何有限群的极限集。它将适用于解决有关这些群体的僵化问题。关于Hadamard流形的研究涉及到Hadamard流形之间的每个拟距离是否离双Lipschitz同胚有限距离的问题。所提出的关于负曲可解Lie群和Hadamard流形的项目是PI在这些主题上先前工作的继续。这些项目的一个共同主题是负曲线空间的几何与这些空间的理想边界分析之间的相互作用。几何群论中的问题往往涉及到空间或映射的大尺度性质,而在分析中,主要关注的往往是局部性质。令人惊讶的是,这些都与具有负曲率的空间相关:负曲线空间具有理想边界,并且空间的大尺度属性编码在理想边界的局部结构中。PI建议通过使用几何分析研究理想边界来研究负曲线空间的大尺度性质。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Xiangdong Xie其他文献
The Tits boundary of a CAT(0) 2-complex
CAT(0) 2 复形的 Tits 边界
- DOI:
- 发表时间:
2005 - 期刊:
- 影响因子:0
- 作者:
Xiangdong Xie - 通讯作者:
Xiangdong Xie
A Tukia-type theorem for nilpotent Lie groups and quasi-isometric rigidity of solvable groups
幂零李群的一个图基亚型定理以及可解群的拟等距刚性
- DOI:
10.1016/j.aim.2025.110202 - 发表时间:
2025-05-01 - 期刊:
- 影响因子:1.500
- 作者:
Tullia Dymarz;David Fisher;Xiangdong Xie - 通讯作者:
Xiangdong Xie
Groups Acting on CAT(0) Square Complexes
- DOI:
10.1007/s10711-004-1527-7 - 发表时间:
2004-12-01 - 期刊:
- 影响因子:0.500
- 作者:
Xiangdong Xie - 通讯作者:
Xiangdong Xie
Quasi-isometric rigidity of a class of right-angled Coxeter groups
一类直角 Coxeter 群的拟等距刚度
- DOI:
10.1090/proc/14743 - 发表时间:
2018 - 期刊:
- 影响因子:1
- 作者:
Jordan C Bounds;Xiangdong Xie - 通讯作者:
Xiangdong Xie
Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley-Martin Functional Responses
具有克劳利-马丁功能反应的专性共生共生模型的动态行为
- DOI:
10.3390/axioms11060298 - 发表时间:
2022 - 期刊:
- 影响因子:2
- 作者:
Lili Xu;Yalong Xue;Xiangdong Xie;Qifa Lin - 通讯作者:
Qifa Lin
Xiangdong Xie的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Xiangdong Xie', 18)}}的其他基金
49th Spring Topology and Dynamics Conference
第49届春季拓扑与动力学会议
- 批准号:
1539762 - 财政年份:2015
- 资助金额:
$ 6.26万 - 项目类别:
Standard Grant
Rigidity in negative curvature and quasiconformal analysis
负曲率刚性和拟共形分析
- 批准号:
1265735 - 财政年份:2012
- 资助金额:
$ 6.26万 - 项目类别:
Standard Grant
相似国自然基金
5'-tRF-GlyGCC通过SRSF1调控RNA可变剪切促三阴性乳腺癌作用机制及干预策略
- 批准号:82372743
- 批准年份:2023
- 资助金额:49.00 万元
- 项目类别:面上项目
染色体结构维持蛋白1在端粒DNA双链断裂损伤修复中的作用及其机理
- 批准号:31801145
- 批准年份:2018
- 资助金额:25.0 万元
- 项目类别:青年科学基金项目
基于个体分析的投影式非线性非负张量分解在高维非结构化数据模式分析中的研究
- 批准号:61502059
- 批准年份:2015
- 资助金额:19.0 万元
- 项目类别:青年科学基金项目
PKCzeta-抑制肽对缺血性损伤的神经保护作用及其机制
- 批准号:30870794
- 批准年份:2008
- 资助金额:35.0 万元
- 项目类别:面上项目
相似海外基金
CAREER: Large scale geometry and negative curvature
职业:大规模几何和负曲率
- 批准号:
2340341 - 财政年份:2024
- 资助金额:
$ 6.26万 - 项目类别:
Continuing Grant
MicroRNA-375 regulation of enteroendocrine cell biology in diet-induced obesity and bariatric surgery
MicroRNA-375对饮食诱导肥胖和减肥手术中肠内分泌细胞生物学的调节
- 批准号:
10377349 - 财政年份:2021
- 资助金额:
$ 6.26万 - 项目类别:
MicroRNA-375 regulation of enteroendocrine cell biology in diet-induced obesity and bariatric surgery
MicroRNA-375对饮食诱导肥胖和减肥手术中肠内分泌细胞生物学的调节
- 批准号:
10627745 - 财政年份:2021
- 资助金额:
$ 6.26万 - 项目类别:
Surface group representations and geometry of negative curvature
负曲率的曲面组表示和几何
- 批准号:
20K03610 - 财政年份:2020
- 资助金额:
$ 6.26万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Challenges in Negative and Nonpositive Curvature
负曲率和非正曲率的挑战
- 批准号:
1906538 - 财政年份:2019
- 资助金额:
$ 6.26万 - 项目类别:
Continuing Grant
Conference on Aspects of Non-Positive and Negative Curvature in Group Theory
群论中非正曲率和负曲率方面的会议
- 批准号:
1856388 - 财政年份:2019
- 资助金额:
$ 6.26万 - 项目类别:
Standard Grant
Trees, cubical complexes, and generalisations of coarse negative curvature in group theory
群论中的树、立方复形和粗负曲率的推广
- 批准号:
2123260 - 财政年份:2018
- 资助金额:
$ 6.26万 - 项目类别:
Studentship
Negative Curvature in Fiber Bundles and Counting Problems
纤维束的负曲率和计数问题
- 批准号:
1708279 - 财政年份:2017
- 资助金额:
$ 6.26万 - 项目类别:
Standard Grant
Negative Curvature in Fiber Bundles and Counting Problems
纤维束的负曲率和计数问题
- 批准号:
1744551 - 财政年份:2017
- 资助金额:
$ 6.26万 - 项目类别:
Standard Grant
EAPSI: Surface Subgroups in Gromov-Thurston Manifolds and Brownian Motion in Riemannian Manifolds of Negative Curvature
EAPSI:格罗莫夫-瑟斯顿流形中的表面子群和负曲率黎曼流形中的布朗运动
- 批准号:
1614366 - 财政年份:2016
- 资助金额:
$ 6.26万 - 项目类别:
Fellowship Award