Geometric Analysis in Conformal Geometry and Fully Nonlinear Elliptic Partial Differential Equations
共形几何和全非线性椭圆偏微分方程中的几何分析
基本信息
- 批准号:1612015
- 负责人:
- 金额:$ 18.05万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2016
- 资助国家:美国
- 起止时间:2016-09-01 至 2020-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The principal investigator's research interest lies at the intersection of conformal geometry and partial differential equations. Conformal geometry is the study of the set of angle-preserving transformations on a space. One focus will be on so-called conformal invariants, which form an important machinery from physicists' point of view and have deep connection to fundamental principles in general relativity. The mass concentration, a phenomenon that has widely appeared in biological and physical sciences, will also be at the center of the investigation. One of the main goals will be to connect different subfields in differential geometry. The generalization will significantly enlarge the scope of the applications.The project research aims to understand basic questions in conformal geometry by using partial differential equations. This includes problems of constructing and classifying conformal invariants, which originated from mathematical physics. It also includes studying the relationship between conformal invariants and other geometric quantities, and establishing geometric inequalities. The PI intends to develop weight theory in order to refine the analytic study of conformal invariants. She will also investigate global rigidity associated to extrinsic curvatures of higher orders on submanifolds.
首席研究员的研究兴趣在于共形几何和偏微分方程的交叉。保角几何是研究空间上保角变换的集合。其中一个重点将放在所谓的共形不变量上,从物理学家的角度来看,它构成了一个重要的机制,与广义相对论的基本原理有着深刻的联系。在生物和物理科学中广泛出现的质量集中现象也将成为调查的中心。主要目标之一是将微分几何中的不同子领域联系起来。这种概括将大大扩大应用的范围。本课题旨在利用偏微分方程来理解保形几何的基本问题。这包括构造和分类共形不变量的问题,它起源于数学物理。它还包括研究保形不变量与其他几何量之间的关系,建立几何不等式。PI打算发展权理论,以完善共形不变量的解析研究。她还将研究与子流形上高阶外在曲率相关的全局刚度。
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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Yi Wang其他文献
Synthesis analysis of frequency selective surface using the generalized sheet transition conditions
使用广义片过渡条件的频率选择表面综合分析
- DOI:
10.1002/mmce.22707 - 发表时间:
2021-04 - 期刊:
- 影响因子:1.7
- 作者:
Shi Chen;Yi Wang;Huangyan Li;Xiaoxing Fang;Qunsheng Cao - 通讯作者:
Qunsheng Cao
[Aging affects early stage direction selectivity of MT cells in rhesus monkeys].
衰老影响恒河猴MT细胞早期方向选择性
- DOI:
10.3724/sp.j.1141.2012.05498 - 发表时间:
2013 - 期刊:
- 影响因子:0
- 作者:
Zhen Liang;Yue Chen;Xue Meng;Yi Wang;Baozhuo Zhou;Ying;Wenxuan He - 通讯作者:
Wenxuan He
Shared and distinct reward neural mechanisms among patients with schizophrenia, major depressive disorder, and bipolar disorder: an effort-based functional imaging study
精神分裂症、重度抑郁症和双相情感障碍患者共享和独特的奖励神经机制:一项基于努力的功能成像研究
- DOI:
10.1007/s00406-021-01376-3 - 发表时间:
2022-01 - 期刊:
- 影响因子:4.7
- 作者:
Yan-yu Wang;Yi Wang;Jia Huang;Xi-he Sun;Xi-zhen Wang;Shu-xian Zhang;Guo-hui Zhu;Simon S. Y. Lui;Eric F. C. Cheung;Hong-wei Sun;Raymond C. K. Chan - 通讯作者:
Raymond C. K. Chan
Multiscale Compressed Block Decomposition Method With Characteristic Basis Function Method and Fast Adaptive Cross Approximation
具有特征基函数法和快速自适应交叉逼近的多尺度压缩块分解方法
- DOI:
10.1109/temc.2018.2801384 - 发表时间:
2019-02 - 期刊:
- 影响因子:2.1
- 作者:
Xiaoxing Fang;Qunsheng Cao;Ye Zhou;Yi Wang - 通讯作者:
Yi Wang
Synthesis and photoluminescence characteristics of novel blue light-emitting naphthalimide derivatives
新型蓝光萘酰亚胺衍生物的合成及光致发光特性
- DOI:
- 发表时间:
- 期刊:
- 影响因子:4.5
- 作者:
Yi Wang;Xiaogen Zhang;Bing Han;et al - 通讯作者:
et al
Yi Wang的其他文献
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{{ truncateString('Yi Wang', 18)}}的其他基金
Collaborative Research: IRES Track I: Undergraduate Interdisciplinary Research in Spain on Smart Connected Systems (UIRiSCS)
合作研究:IRES 第一轨:西班牙智能互联系统本科跨学科研究 (UIRiSCS)
- 批准号:
2153667 - 财政年份:2022
- 资助金额:
$ 18.05万 - 项目类别:
Standard Grant
Programmable Microwave Hardware Based on Liquid Wires (PROGRAMMABLE)
基于液线的可编程微波硬件(PROGRAMMABLE)
- 批准号:
EP/V008382/1 - 财政年份:2021
- 资助金额:
$ 18.05万 - 项目类别:
Research Grant
Arveson-Douglas Conjecture and Its Applications
阿维森-道格拉斯猜想及其应用
- 批准号:
2101370 - 财政年份:2020
- 资助金额:
$ 18.05万 - 项目类别:
Continuing Grant
CAREER: Conformal Geometry and Monge-Ampere Type Equations
职业:共形几何和 Monge-Ampere 型方程
- 批准号:
1845033 - 财政年份:2019
- 资助金额:
$ 18.05万 - 项目类别:
Continuing Grant
Arveson-Douglas Conjecture and Its Applications
阿维森-道格拉斯猜想及其应用
- 批准号:
1900076 - 财政年份:2019
- 资助金额:
$ 18.05万 - 项目类别:
Continuing Grant
Synthesis and new applications of multi-port filtering networks
多端口滤波网络综合及新应用
- 批准号:
EP/M013529/1 - 财政年份:2015
- 资助金额:
$ 18.05万 - 项目类别:
Research Grant
Geometric Inequalities and Fully Nonlinear Elliptic Equations
几何不等式和完全非线性椭圆方程
- 批准号:
1547878 - 财政年份:2014
- 资助金额:
$ 18.05万 - 项目类别:
Standard Grant
Geometric Inequalities and Fully Nonlinear Elliptic Equations
几何不等式和完全非线性椭圆方程
- 批准号:
1205350 - 财政年份:2012
- 资助金额:
$ 18.05万 - 项目类别:
Standard Grant
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