Geometric Flows and Canonical Kahler Metrics

几何流和规范卡勒度量

基本信息

  • 批准号:
    1945869
  • 负责人:
  • 金额:
    $ 8.79万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2019
  • 资助国家:
    美国
  • 起止时间:
    2019-07-01 至 2020-07-31
  • 项目状态:
    已结题

项目摘要

Award: DMS 1710500, Principal Investigator: Bin GuoThe Einstein equations from gravitational theory have a geometric interpretation that picks out a preferred metric to determine lengths and angles on a space. The determination of conditions for solvability of those equations has seen recent progress and continues to pose important open problems in geometry. The projects to be carried out include approaches to those problems through geometric flows that deform the metric on a space in a direction that might lead to a canonical metric, or, alternatively, might develop a singularity that blocks progress toward such a metric.Some of these projects will study the formation of long-time and short-time singularities from Kaehler-Ricci flow which are closely related to the analytic minimal model program proposed by Song and Tian. The conical Kaehler-Einstein equations have been very successful for Fano manifolds, and these projects will investigate the existence and properties of conical canonical Kaehler metrics in algebraic varieties and explore their applications in solving open problems in algebraic geometry. Another line of work will study coupled systems of parabolic type which originated from general relativity in physics. The solutions to the coupled systems will yield Einstein vacuum metrics and shed light on the structure of the underlying space.
奖项:DMS 1710500,首席研究员:郭斌来自引力理论的爱因斯坦方程有一个几何解释,选择一个首选的度量来确定空间上的长度和角度。 这些方程的可解性条件的确定最近取得了进展,并继续在几何中提出重要的开放问题。将要进行的项目包括通过几何流来解决这些问题的方法,这些几何流使空间上的度量在可能导致规范度量的方向上变形,或者,可能会发展出一个奇点,阻碍这种度量的进展。其中一些项目将研究凯勒的长时间和短时间奇点的形成-Ricci流与Song和Tian提出的解析极小模型程序密切相关。锥形Kaehler-Einstein方程在Fano流形上已经非常成功,这些项目将研究代数簇中锥形正则Kaehler度量的存在性和性质,并探索它们在解决代数几何中的公开问题中的应用。 另一项工作将研究抛物型耦合系统,它起源于物理学中的广义相对论。耦合系统的解将产生爱因斯坦真空度规,并揭示底层空间的结构。

项目成果

期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On the degeneration of asymptotically conical Calabi–Yau metrics
渐近圆锥形卡拉比丘度规的退化
  • DOI:
    10.1007/s00208-021-02229-z
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    1.4
  • 作者:
    Collins, T.
  • 通讯作者:
    Collins, T.
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Bin Guo其他文献

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
Cloning and Characterization of a Novel Avirulence Gene (arp3) from Xanthomonas oryzae pv. oryzae
米黄单胞菌新型无毒基因 (arp3) 的克隆和表征
  • DOI:
    10.1080/10425170410001679174
  • 发表时间:
    2004
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Bin Liang;Teng;Bin Guo;Chen Yang;Luyuan Dai;D. Shen
  • 通讯作者:
    D. Shen
Catalytic synthesis of nanodiamond based on CDC principle: influence of different catalysts on types and sizes
基于CDC原理的纳米金刚石催化合成:不同催化剂对类型和尺寸的影响
  • DOI:
    10.1088/1361-6528/ac0d7f
  • 发表时间:
    2021-06
  • 期刊:
  • 影响因子:
    3.5
  • 作者:
    Bin Guo;Wenyu Wu;Huaxin Ma;Zhao Zhang;Zhi Zhang;Weinan Gao;Wei Zhou;Ruijun Zhang
  • 通讯作者:
    Ruijun Zhang
Retrievals of fine mode light-absorbing carbonaceous aerosols from POLDER/PARASOL observations over East and South Asia
从东亚和南亚 POLDER/PARASOL 观测中反演精细模式光吸收碳质气溶胶
  • DOI:
    10.1016/j.rse.2020.111913
  • 发表时间:
    2020-09
  • 期刊:
  • 影响因子:
    13.5
  • 作者:
    Lei Li;Huizheng Che;Yevgeny Derimian;Oleg Dubovik;Gregory L. Schuster;Cheng Chen;Qiuyue Li;Yaqiang Wang;Bin Guo;Xiaoye Zhang
  • 通讯作者:
    Xiaoye Zhang
Fruit extracts from Phyllanthus emblica accentuate cadmium tolerance and accumulation in Platycladus orientalis: A new natural chelate for phytoextraction.
余甘子的果实提取物增强了侧柏的镉耐受性和积累:一种用于植物提取的新型天然螯合物。
  • DOI:
    10.1016/j.envpol.2021.116996
  • 发表时间:
    2021-03
  • 期刊:
  • 影响因子:
    8.9
  • 作者:
    Bin Guo;Chen Liu;Yicheng Lin;Hua Li;Ningyu Li;Junli Liu;Qinglin Fu;Wenbin Tong;Haiping Yu
  • 通讯作者:
    Haiping Yu

Bin Guo的其他文献

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{{ truncateString('Bin Guo', 18)}}的其他基金

Canonical Kahler metrics and complex Monge-Ampere equations
规范卡勒度量和复杂的 Monge-Ampere 方程
  • 批准号:
    2303508
  • 财政年份:
    2023
  • 资助金额:
    $ 8.79万
  • 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:
    $ 8.79万
  • 项目类别:
    Standard Grant

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Geometric Flows and Canonical Kahler Metrics
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