On geometric analysis related to the Cosmic Censorship Conjecture

论与宇宙审查猜想相关的几何分析

基本信息

批准号：
23654061
负责人：
YAMADA Sumio
金额：
$ 2.16万
依托单位：
Gakushuin University (2013)Tohoku University (2011-2012)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Challenging Exploratory Research
财政年份：
2011
资助国家：
日本
起止时间：
2011 至 2013
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23654061/
关键词：
アインシュタイン方程式発展方程式極小曲面リーマン計量コーシー初期条件リーマン計量の変形理論共形幾何ハミルトン力学系国際研究者交流（アメリカ）国際研究者交流（オーストラリア）国際情報交換（アメリカ）国際情報交換（中国）

项目摘要

Based on ideas inherent in two major advances in the field of geometric analysis, namely, Perelman's resolution of Ricci flow, and Bray's proof of Riemannian Penrose inequality using conformal deformation of Riemannian metrics, the PI has succeeded in generalizing the Penrose inequality, concerning the solution of the Einstein-Maxwell equation. The Investigator Nakamura has also obtained a set of interesting results in the field of nonlinear hyperbolic partial differential equations, which are closely related to the Einstein equation.Under the support of the current grant, two international meetings were organized in Japan, and together with attending academic meetings abroad, the investigators Yamada and Nakamura established opportunities for exchanges of ideas, which led to the collaboration with Gilbert Weinstein and Marcus Khuri, which in turn became the major work described above.

基于几何分析领域的两个主要进步的思想，即佩雷尔曼（Perelman）解决里奇（Ricci）流动的解决，以及布雷使用riemannian Metrics的综合变形的Riemannian Penrose不平等的证明，PI成功地使Penrose的不平等现象成功地使eIntein Maxwell sore noreine streation Maxwell。 The Investigator Nakamura has also obtained a set of interesting results in the field of nonlinear hyperbolic partial differential equations, which are closely related to the Einstein equation.Under the support of the current grant, two international meetings were organized in Japan, and together with attending academic meetings abroad, the investigators Yamada and Nakamura established opportunities for exchanges of ideas, which led to the collaboration with Gilbert Weinstein and Marcus库里（Khuri）又成为上述主要工作。

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）

Lower bounds for the area of black holes in terms of mass, charge, and angular momentum

黑洞面积的质量、电荷和角动量下限

DOI：
10.1103/physrevd.88.024048
发表时间：
2013
期刊：
Physical Review D
影响因子：
5
作者：
Sergio Dain;Marcus Khuri;Gilbert Weinstein;Sumio Yamada
通讯作者：
Sumio Yamada

The Cauchy problem for semi-linear Klein-Gordon equations in de Sitter spacetime

德西特时空中半线性克莱因-戈登方程的柯西问题

DOI：
发表时间：
2014
期刊：
Journal of Mathematical Analysis and Applications
影响因子：
1.3
作者：
T. Nagai;T. Ogawa,;T. Nodera;Makoto Nakamura
通讯作者：
Makoto Nakamura

On Variational Formulation of Free Boundaries

关于自由边界的变分公式

DOI：
发表时间：
2011
期刊：
影响因子：
0
作者：
Y.Mizumura;T.Tanimori et al.;Sumio Yamada
通讯作者：
Sumio Yamada

A counterexample to a Penrose inequality conjectured by Gibbons.

吉本斯猜想的彭罗斯不等式的反例。

DOI：
发表时间：
2011
期刊：
Classical and Quantum Gravity
影响因子：
3.5
作者：
Sergio Dain;Gilbert Weinstein;Sumio Yamada
通讯作者：
Sumio Yamada

On variational characterization of exact solutions in general relativity

广义相对论中精确解的变分表征

DOI：
发表时间：
2013
期刊：
影响因子：
0
作者：
Kotani, M.;Imai, T.;Katayama, H.;Yui, Y.;Tange, Y.;Kaneda, H.;Nakagawa, T.;Enya, K.;Shinya Nishibata;Sumio Yamada
通讯作者：
Sumio Yamada