Problems in General Relativity and Geometric Flows
广义相对论和几何流问题
基本信息
- 批准号:1810856
- 负责人:
- 金额:$ 23.53万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-07-01 至 2023-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project concerns investigations of fundamental problems at the interface of general relativity, geometry, and differential equations. Einstein's theory of general relativity describes how the spacetime is curved by gravitation. The language of his theory is geometry and the phenomenon is governed by his eponymous equation. There have been great advances in both theoretical and experimental aspects of general relativity, for example the recent detection of gravitational waves by LIGO. However, due to the complexity of Einstein's equation, most of our knowledge of the universe are global and large scale, such as the observation of an astrophysical event from a very faraway distance. Recently, the PI and his collaborators applied the tools of geometry and differential equations to give the most precise measurement of gravitational energy and mass on any finitely extended region of the universe. This is essential in understanding the fine and local structure of our universe, with applications in, for example, GPS technology and space exploration. It is also crucial in studying non-isolated large-scale phenomena such as black hole mergers and collisions. The success of this project will deepen our understanding of gravitational energy/mass and the nonlinear local/global nature of the spacetime. The PI also plans to study geometric flows, which are differential equations that model how a geometric shape deforms and evolves to an optimal form in the most efficient way. The PI has been engaging himself in educating a diversified body of graduate students and young researchers, and the project will be instrumental for his continued efforts along this direction.The PI plans to resolve several outstanding problems in general relativity and geometric flows by the method of geometric analysis. In particular, the quasilocal mass definition the PI discovered with Yau will be a key ingredient in this research. Immediate goals include proving the general invariant mass conjecture, establishing a positive mass theorem for the Robinson-Trautman spacetime and the linear stability of higher dimensional Schwarzschild spacetimes, and the solution of a conjecture of Arnol'd by the Lagrangian mean curvature flow. This research project will also advance our understanding of nonlinear partial differential systems such as the optimal isometric embedding equation, the mean curvature flow, and the Einstein equation.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.
这个项目涉及在广义相对论、几何和微分方程界面上的基本问题的研究。爱因斯坦的广义相对论描述了时空是如何被引力弯曲的。他的理论语言是几何学,这种现象是由他的同名方程控制的。广义相对论在理论和实验方面都取得了巨大的进步,例如最近LIGO探测到的引力波。然而,由于爱因斯坦方程的复杂性,我们对宇宙的大部分认识都是全局的和大尺度的,比如从非常遥远的距离观察一个天体物理事件。最近,PI和他的合作者运用几何和微分方程的工具,对宇宙中任何有限扩展区域的引力能和质量进行了最精确的测量。这对于理解我们宇宙的精细和局部结构是至关重要的,例如在GPS技术和空间探索中的应用。它在研究非孤立的大规模现象,如黑洞合并和碰撞方面也至关重要。该项目的成功将加深我们对引力能/质量和时空的非线性局域/全局性质的理解。PI还计划研究几何流,这是一种微分方程,它模拟几何形状如何以最有效的方式变形并演变成最佳形式。PI一直致力于培养多样化的研究生和年轻研究人员,该项目将有助于他继续朝着这个方向努力。PI计划用几何分析的方法解决广义相对论和几何流中的几个突出问题。特别是,PI与Yau一起发现的准局部质量定义将是本研究的关键因素。近期目标包括证明一般不变质量猜想,建立Robinson-Trautman时空的正质量定理和高维史瓦西时空的线性稳定性,以及用拉格朗日平均曲率流求解Arnol猜想。该研究项目也将促进我们对非线性偏微分系统的理解,如最优等距嵌入方程、平均曲率流和爱因斯坦方程。该奖项反映了美国国家科学基金会的法定使命,并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(9)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Evolution of Angular Momentum and Center of Mass at Null Infinity
- DOI:10.1007/s00220-021-04053-7
- 发表时间:2021-02
- 期刊:
- 影响因子:2.4
- 作者:Po-Ning Chen;Jordan Keller;Mu-Tao Wang;Ye-Kai Wang;S. Yau
- 通讯作者:Po-Ning Chen;Jordan Keller;Mu-Tao Wang;Ye-Kai Wang;S. Yau
Quasi-local mass and isometric embedding with reference to a static spacetime
- DOI:10.2969/aspm/08510453
- 发表时间:2020-10
- 期刊:
- 影响因子:0
- 作者:Mu-Tao Wang
- 通讯作者:Mu-Tao Wang
Global uniqueness of the minimal sphere in the Atiyah–Hitchin manifold
阿蒂亚希钦流形中最小球面的全局唯一性
- DOI:10.4310/mrl.2022.v29.n3.a10
- 发表时间:2022
- 期刊:
- 影响因子:1
- 作者:Tsai, Chung-Jun;Wang, Mu-Tao
- 通讯作者:Wang, Mu-Tao
Linear Stability of Higher Dimensional Schwarzschild Spacetimes: Decay of Master Quantities
- DOI:10.1007/s40818-020-00083-x
- 发表时间:2018-09
- 期刊:
- 影响因子:2.8
- 作者:Pei-Ken Hung;Jordan Keller;Mu-Tao Wang
- 通讯作者:Pei-Ken Hung;Jordan Keller;Mu-Tao Wang
Quasi-local mass on unit spheres at spatial infinity
空间无穷远单位球体上的准局部质量
- DOI:10.4310/cag.2022.v30.n4.a2
- 发表时间:2022
- 期刊:
- 影响因子:0.7
- 作者:Chen, Po-Ning;Wang, Mu-Tao;Wang, Ye-Kai;Yau, Shing-Tung
- 通讯作者:Yau, Shing-Tung
{{
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 }}
Mu-Tao Wang其他文献
Gravitational energy seen by quasilocal observers
- DOI:
10.1088/0264-9381/28/11/114011 - 发表时间:
2011-06 - 期刊:
- 影响因子:3.5
- 作者:
Mu-Tao Wang - 通讯作者:
Mu-Tao Wang
The Minkowski Formula and the Quasi-Local Mass
- DOI:
10.1007/s00023-019-00766-7 - 发表时间:
2019-02-07 - 期刊:
- 影响因子:1.300
- 作者:
Po-Ning Chen;Mu-Tao Wang;Shing-Tung Yau - 通讯作者:
Shing-Tung Yau
Gauss Maps of the Mean Curvature Flow
- DOI:
10.4310/mrl.2003.v10.n3.a2 - 发表时间:
2002-09 - 期刊:
- 影响因子:1
- 作者:
Mu-Tao Wang - 通讯作者:
Mu-Tao Wang
Lectures on mean curvature ows in higher codimensions
- DOI:
- 发表时间:
2011-04 - 期刊:
- 影响因子:0
- 作者:
Mu-Tao Wang - 通讯作者:
Mu-Tao Wang
On graphic Bernstein type results in higher codimension
- DOI:
10.1090/s0002-9947-02-03108-2 - 发表时间:
2002-02 - 期刊:
- 影响因子:1.3
- 作者:
Mu-Tao Wang - 通讯作者:
Mu-Tao Wang
Mu-Tao Wang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('Mu-Tao Wang', 18)}}的其他基金
Mass/Momentum beyond Classical Gravity and Submanifolds of Higher Codimensions
超越经典引力的质量/动量和更高维数的子流形
- 批准号:
2104212 - 财政年份:2021
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
Applications of geometric analysis to general relativity and geometric flows
几何分析在广义相对论和几何流中的应用
- 批准号:
1405152 - 财政年份:2014
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
Problems in general relativity and geometric flows
广义相对论和几何流中的问题
- 批准号:
1105483 - 财政年份:2011
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
Geometric analysis problems related to surfaces in mathematical physics
数学物理中与曲面相关的几何分析问题
- 批准号:
0904281 - 财政年份:2009
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
Geometry and PDE of submanifolds of higher codimensions
高余维子流形的几何和偏微分方程
- 批准号:
0605115 - 财政年份:2006
- 资助金额:
$ 23.53万 - 项目类别:
Continuing Grant
Mean curvature flows in higher codimensions
较高余维中的平均曲率流
- 批准号:
0306049 - 财政年份:2003
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
相似国自然基金
Toward a general theory of intermittent aeolian and fluvial nonsuspended sediment transport
- 批准号:
- 批准年份:2022
- 资助金额:55 万元
- 项目类别:
相似海外基金
MATHEMATICAL PROBLEMS IN GENERAL RELATIVITY
广义相对论中的数学问题
- 批准号:
2304445 - 财政年份:2023
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
Geometric Boundary Value Problems in General Relativity
广义相对论中的几何边值问题
- 批准号:
2304966 - 财政年份:2023
- 资助金额:
$ 23.53万 - 项目类别:
Standard Grant
Singularity formation in general relativity, and geometric inverse problems.
广义相对论中奇点的形成和几何逆问题。
- 批准号:
RGPIN-2020-05108 - 财政年份:2022
- 资助金额:
$ 23.53万 - 项目类别:
Discovery Grants Program - Individual
Mathematical problems in general relativity
广义相对论中的数学问题
- 批准号:
RGPIN-2017-06103 - 财政年份:2021
- 资助金额:
$ 23.53万 - 项目类别:
Discovery Grants Program - Individual
Singularity formation in general relativity, and geometric inverse problems.
广义相对论中奇点的形成和几何逆问题。
- 批准号:
RGPIN-2020-05108 - 财政年份:2021
- 资助金额:
$ 23.53万 - 项目类别:
Discovery Grants Program - Individual
Mathematical Problems in General Relativity
广义相对论中的数学问题
- 批准号:
2005435 - 财政年份:2020
- 资助金额:
$ 23.53万 - 项目类别:
Continuing Grant
Mathematical problems in general relativity
广义相对论中的数学问题
- 批准号:
RGPIN-2017-06103 - 财政年份:2020
- 资助金额:
$ 23.53万 - 项目类别:
Discovery Grants Program - Individual
Singularity formation in general relativity, and geometric inverse problems.
广义相对论中奇点的形成和几何逆问题。
- 批准号:
RGPIN-2020-05108 - 财政年份:2020
- 资助金额:
$ 23.53万 - 项目类别:
Discovery Grants Program - Individual
Mathematical problems in general relativity
广义相对论中的数学问题
- 批准号:
2478319 - 财政年份:2020
- 资助金额:
$ 23.53万 - 项目类别:
Studentship
Mathematical problems in general relativity
广义相对论中的数学问题
- 批准号:
RGPIN-2017-06103 - 财政年份:2019
- 资助金额:
$ 23.53万 - 项目类别:
Discovery Grants Program - Individual