课题基金 / 基金详情

Mathematical Sciences: Analysis and the Geometry of Submanifolds/Injectivity Problems in Geometry

Mathematical Sciences: Analysis and the Geometry of Submanifolds/Injectivity Problems in Geometry
数学科学:几何中子流形/内射性问题的分析和几何
批准号:
9625392
负责人:
Brian Smyth
金额:
$10.5万
依托单位:
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1996
资助国家:
美国
项目状态:
已结题
起止时间:
1996-08-01 至 1999-07-31

项目摘要

项目成果

Brian Smyth的其他基金

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中文摘要
翻译
小行星9625392 这个项目是在微分几何和子流形理论领域。研究人员计划追求Caratheodory猜想(3-空间中的球体必须至少有两个脐点),两个变量中连续可微映射的稳定性猜想,以及极小曲面的函数理论方面。此外,他们将检查超曲面的主曲率。 子流形理论研究欧氏空间中曲线和(超)曲面的各种性质-度量、拓扑、全局和局部。子流形理论中的一个重要考虑是了解子流形的外在性质如何与其内在性质相互作用。这个项目包含两个杰出的acquitures在这一领域;试图接口与其他领域的数学,如动力系统理论和代数几何。
英文摘要
9625392 Smyth This project lies in the area of differential geometry and submanifold theory. The investigator plans to pursue the Caratheodory conjecture (a sphere in 3-space must have at least two umbilics), the stability conjecture for continuously differentiable maps in two variables, and function theoretic aspects of minimal surfaces. In addition, they will examine principal curvatures of hypersurfaces. Submanifold theory deals with various properties - metric, topological, global and local - of curves and (hyper-) surfaces lying in Euclidean and sometimes more general spaces. An important consideration in submanifold theory is to understand how extrinsic properties of a submanifold interact with its intrinsic properties. This project contains two of the outstanding conjectures in this area; attempts to interface with other areas of mathematics such as dynamical systems theory and algebraic geometry.
期刊论文(0)
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会议论文
Problems in surface theory/ membranes/hypersurface singularities
  • 批准号:
    0071729
  • 项目类别:
    Standard Grant
  • 资助金额:
    $6.0万
  • 财政年份:
    2000
  • 负责人:
    Brian Smyth
  • 依托单位:
Mathematical Sciences: Geometry of Submanifolds/InjectivityProblems in Geometry
  • 批准号:
    9204946
  • 项目类别:
    Standard Grant
  • 资助金额:
    $12.0万
  • 财政年份:
    1992
  • 负责人:
    Brian Smyth
  • 依托单位:
Mathematical Sciences: Complete Surfaces in Three-Space
  • 批准号:
    8702383
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $13.13万
  • 财政年份:
    1987
  • 负责人:
    Brian Smyth
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences