Canonical Kahler metrics and complex Monge-Ampere equations
规范卡勒度量和复杂的 Monge-Ampere 方程
基本信息
- 批准号:2303508
- 负责人:
- 金额:$ 15.29万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-08-15 至 2026-07-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
The project will focus on addressing open problems in geometric analysis and exploring their applications in various fields such as geometry, topology and mathematical physics. These problems play a central role in active areas of research in mathematics, including differential geometry, partial differential equations (PDE), and high-dimensional supergravity. Given the interdisciplinary nature of this project, it will foster collaborations among researchers from various disciplines, and the outcomes of the project will introduce novel approaches and provide valuable insights into the analytic study of the geometry of singular varieties. An important objective of the project is to establish a foundation for the integration of research and education, enriching the mathematics curriculum and enhancing the mathematics education at Rutgers - Newark. In line with this objective, the Principal Investigator (PI) will organize seminars and deliver lectures, aiming to contribute towards the advancement of mathematics education nationwide. The PI will also engage in mentoring at at high school, undergraduate, and graduate levels. The PI will continue to develop novel approaches in the regularity theory for linear and fully nonlinear PDEs on complex manifolds, with a specific focus on the complex Monge-Ampere equations and the associated Kahler metrics. The geometry of these metrics will be investigated from both analytic and geometric perspectives. An emphasis will be placed on studying the degeneration of a family of Kahler metrics, including the geometric convergence of Kahler-Ricci flow and other flows arising from geometry and physics. To this end, the PI will advance the techniques of auxiliary differential equations, aiming to analyze the compactness of the space of the family of Kahler metrics. Along this path, it is expected that new analytic tools such as uniform Poincare and Sobolev inequalities, as well as heat kernel estimates, will be developed. Furthermore, combined with techniques from complex geometry and algebraic geometry, these tools will be employed to investigate the asymptotic behavior of metrics near singularities. In addition, the PI will continue to explore the parabolic approach, introduced by the PI and collaborators, in high-dimensional supergravity. This exploration aims to discover new ansatz and construct new solutions to the coupled systems, thereby deepening the understanding of the underlying space.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该项目将侧重于解决几何分析中的开放问题,并探索其在几何,拓扑和数学物理等各个领域的应用。这些问题在数学研究的活跃领域中起着核心作用,包括微分几何,偏微分方程(PDE)和高维超引力。鉴于该项目的跨学科性质,它将促进来自不同学科的研究人员之间的合作,该项目的成果将引入新的方法,并为奇异品种几何的分析研究提供有价值的见解。该项目的一个重要目标是为研究和教育的整合奠定基础,丰富数学课程,提高罗格斯-纽瓦克的数学教育。根据这一目标,首席研究员(PI)将组织研讨会和讲座,旨在促进全国数学教育的进步。PI还将在高中,本科和研究生阶段进行指导。PI将继续在复杂流形上的线性和完全非线性偏微分方程的正则性理论中开发新的方法,特别关注复杂的Monge-Ampere方程和相关的Kahler度量。这些指标的几何将从分析和几何的角度进行研究。 重点将放在研究一族Kahler度量的退化,包括Kahler-Ricci流的几何收敛和其他由几何和物理引起的流。为此,PI将推进辅助微分方程的技术,旨在分析Kahler度量族空间的紧致性。沿着这条道路,预计新的分析工具,如统一庞加莱和Sobolev不等式,以及热核估计,将被开发。此外,结合从复几何和代数几何的技术,这些工具将被用来调查的渐近行为的度量附近的奇点。此外,PI将继续探索由PI及其合作者在高维超引力中引入的抛物线方法。该奖项反映了NSF的法定使命,通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。
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)
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Bin Guo其他文献
Eco-friendly non-acid intercalation and exfoliation of graphite to graphene nanosheets in the binary-peroxidant system for EMI shielding
用于 EMI 屏蔽的二元过氧化物体系中石墨与石墨烯纳米片的环保非酸插层和剥离
- DOI:
10.1016/j.cclet.2021.05.064 - 发表时间:
2021-06 - 期刊:
- 影响因子:9.1
- 作者:
Ping Wang;Bin Guo;Zhi Zhang;Weinan Gao;Wei Zhou;Huaxin Ma;Wenyu Wu;Junfeng Han;Ruijun Zhang - 通讯作者:
Ruijun Zhang
Event-triggered adaptive fuzzy tracking control for a class of fractional-order uncertain nonlinear systems with external disturbance
一类有外扰的分数阶不确定非线性系统的事件触发自适应模糊跟踪控制
- DOI:
10.1016/j.chaos.2022.112393 - 发表时间:
2022-08 - 期刊:
- 影响因子:7.8
- 作者:
Xingxing You;Mingyang Shi;Bin Guo;Yuqi Zhu;Wuxing Lai;Songyi Dian;Kai Liu - 通讯作者:
Kai Liu
Smart Cities: Recent Trends, Methodologies, and Applications
智慧城市:最新趋势、方法和应用
- DOI:
10.1155/2017/7090963 - 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
D. Gavalas;Petros Nicopolitidis;A. Kameas;C. Goumopoulos;P. Bellavista;L. Lambrinos;Bin Guo - 通讯作者:
Bin Guo
Gja1 acts downstream of Acvr1 to regulate uterine decidualization via Hand2 in mice
Gja1 作用于 Acvr1 下游,通过 Hand2 调节小鼠子宫蜕膜化
- DOI:
10.1530/joe-16-0583 - 发表时间:
2017 - 期刊:
- 影响因子:4
- 作者:
Haifan Yu;Zhanpeng Yue;Kai Wang;Zhanqing Yang;Hongliang Zhang;Shuang Geng;Bin Guo - 通讯作者:
Bin Guo
Study of the Correlation Between the Doped-Oxygen Species and the Supercapacitive Performance of TiC–CDC Carbon-Based Material
TiC·CDC碳基材料掺杂氧种类与超级电容性能相关性研究
- DOI:
10.1142/s179329201950142x - 发表时间:
2019-11 - 期刊:
- 影响因子:1.2
- 作者:
Yu Gu;Ruijun Zhang;Wenyu Wu;Bin Guo;Ping Wang;Huaxin Ma - 通讯作者:
Huaxin Ma
Bin Guo的其他文献
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{{ truncateString('Bin Guo', 18)}}的其他基金
Geometric Flows and Canonical Kahler Metrics
几何流和规范卡勒度量
- 批准号:
1945869 - 财政年份:2019
- 资助金额:
$ 15.29万 - 项目类别:
Standard Grant
Geometric Flows and Canonical Kahler Metrics
几何流和规范卡勒度量
- 批准号:
1710500 - 财政年份:2017
- 资助金额:
$ 15.29万 - 项目类别:
Standard Grant
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有限时间Kahler-Ricci流与解析极小模型纲领的几何化
- 批准号:
- 批准年份:2022
- 资助金额:30 万元
- 项目类别:青年科学基金项目
整性特殊凯勒结构及其在两类Hyper-Kahler度量上的应用
- 批准号:12271495
- 批准年份:2022
- 资助金额:47 万元
- 项目类别:面上项目
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- 批准号:
- 批准年份:2020
- 资助金额:52 万元
- 项目类别:面上项目
几类非Kahler复流形的研究
- 批准号:11701414
- 批准年份:2017
- 资助金额:23.0 万元
- 项目类别:青年科学基金项目
复toric流形和复toric orbifold 上的极值 Kahler 度量问题
- 批准号:11626050
- 批准年份:2016
- 资助金额:3.0 万元
- 项目类别:数学天元基金项目
曲率几乎非负的紧致Kahler流形的几何与拓扑
- 批准号:11601044
- 批准年份:2016
- 资助金额:19.0 万元
- 项目类别:青年科学基金项目
度量几何及其在Kahler几何中的应用
- 批准号:11501501
- 批准年份:2015
- 资助金额:18.0 万元
- 项目类别:青年科学基金项目
Kahler 曲面中特殊曲面的研究
- 批准号:11471014
- 批准年份:2014
- 资助金额:65.0 万元
- 项目类别:面上项目
Kahler几何与辛拓扑中若干问题的研究
- 批准号:11371345
- 批准年份:2013
- 资助金额:50.0 万元
- 项目类别:面上项目
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- 批准号:11271343
- 批准年份:2012
- 资助金额:60.0 万元
- 项目类别:面上项目
相似海外基金
Research on the relationship between canonical metrics and deformations of complex structures on compact Kahler manifolds
紧卡勒流形上复杂结构正则度量与变形关系研究
- 批准号:
22K03316 - 财政年份:2022
- 资助金额:
$ 15.29万 - 项目类别:
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Geometric Flows and Canonical Kahler Metrics
几何流和规范卡勒度量
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$ 15.29万 - 项目类别:
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具有非消失 Futaki 不变量的 Fano 流形的规范 Kahler 度量
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19J01482 - 财政年份:2019
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规范卡勒度量和模空间
- 批准号:
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