Research in Differential Geometry and Topology

微分几何与拓扑研究

基本信息

  • 批准号:
    9803206
  • 负责人:
  • 金额:
    $ 7.83万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1998
  • 资助国家:
    美国
  • 起止时间:
    1998-08-01 至 2001-07-31
  • 项目状态:
    已结题

项目摘要

Abstract Proposal: DMS-9803206 Principal Investigator: William H. Meeks III The general goal of this research proposal is to get a deeper understanding of the global geometry of surfaces in three-dimensional Euclidean space. One goal is to understand the topology, asymptotic geometry and conformal structure of properly embedded minimal surfaces. A second important goal is to apply these results to understand the convergence of bounded genus minimal surfaces in three-manifolds. The field of minimal surfaces has its roots based on geometric studies by the major mathematicians of the previous century. However, the new analytic and geometric techniques developed in the past twenty years have made the theory of minimal surfaces an essential research tool in other fields. These fields include Topology, Algebraic Geometry, geometry of black holes and elementary particle Physics. I propose to characterize how these infinite surfaces behave geometrically and to classify them. Recently certain examples of these surfaces were used to model interfaces in coblock polymers and one of my classification results shows that these are the only possible examples. The primary goal of this proposal is to prove some beautiful conjectures concerning these surfaces, whose solutions will have important applications to other parts of Mathematics and Science.
摘要提案:DMS-9803206首席研究员:William H. Meeks III本研究提案的总体目标是更深入地了解三维欧几里得空间中表面的整体几何形状。一个目标是了解适当嵌入的最小曲面的拓扑结构、渐近几何和共形结构。第二个重要的目标是应用这些结果来理解三流形中有界最小曲面的收敛性。极小曲面的研究植根于上个世纪主要数学家的几何研究。然而,近二十年来发展起来的新的解析技术和几何技术使最小曲面理论成为其他领域必不可少的研究工具。这些领域包括拓扑学、代数几何、黑洞几何和基本粒子物理。我建议描述这些无限曲面的几何行为,并对它们进行分类。最近,这些表面的某些例子被用来模拟共嵌段聚合物的界面,我的分类结果之一表明,这些是唯一可能的例子。这个提议的主要目标是证明一些关于这些表面的美丽猜想,这些猜想的解将在数学和科学的其他部分有重要的应用。

项目成果

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William Meeks其他文献

MP67-12 PEYRONIE'S DISEASE IS ASSOCIATED WITH INCREASED IMMUNE REACTIVITY: ANALYSIS OF UNITED STATES CLAIMS DATA
  • DOI:
    10.1016/j.juro.2018.02.2196
  • 发表时间:
    2018-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Taylor P. Kohn;Daniel Pichardo;Katherine M. Rodriguez;William Meeks;Larry I. Lipshultz;Alexander W. Pastuszak
  • 通讯作者:
    Alexander W. Pastuszak
MP96-14 ANALYSIS OF NATIONAL TRENDS IN HOSPITAL ACQUIRED CONDITIONS FOLLOWING MAJOR UROLOGIC SURGERY BEFORE AND AFTER IMPLEMENTATION OF THE HOSPITAL ACQUIRED CONDITION REDUCTION PROGRAM
  • DOI:
    10.1016/j.juro.2017.02.3037
  • 发表时间:
    2017-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Temitope Rude;Nicholas Donin;Matthew Cohn;William Meeks;Scott Gulig;James Wysock;Danil Makarov;Marc Bjurlin
  • 通讯作者:
    Marc Bjurlin
INSANE IN THE MEMBRANE: THE ROLE OF CATHETERIZATION IN THE DIAGNOSIS OF A SUBAORTIC MEMBRANE
  • DOI:
    10.1016/s0735-1097(24)06091-1
  • 发表时间:
    2024-04-02
  • 期刊:
  • 影响因子:
  • 作者:
    Rebecca Kocak;Christina Romano;Cara Joseph;Meer Fakhry;William Meeks;Ninad M. Zaman;Muhammad Mohyuddin;Hata Mujadzic;Gabrielle Rhinehart;Patrick Anthony Xavier Hall
  • 通讯作者:
    Patrick Anthony Xavier Hall
YOU UNDERESTIMATE MY POWER: EMPHASIZING DYSSYNCHRONY IN THE ERA OF SYNCHRONY FOR HCM PATIENTS
  • DOI:
    10.1016/s0735-1097(24)05664-x
  • 发表时间:
    2024-04-02
  • 期刊:
  • 影响因子:
  • 作者:
    Christina Romano;Dominic J. Vacca;William Meeks;Ninad M. Zaman;Rebecca Kocak;Muhammad Mohyuddin;Hata Mujadzic;Gabrielle Rhinehart;Meer Fakhry
  • 通讯作者:
    Meer Fakhry
FORGOTTEN CAUSE OF CHEST PAIN DUE TO A RARE COMPLICATION OF A COMMON PROCEDURE
  • DOI:
    10.1016/s0735-1097(23)04408-x
  • 发表时间:
    2023-03-07
  • 期刊:
  • 影响因子:
  • 作者:
    Muhammad Mohyuddin;Ninad M. Zaman;Meer Fakhry;Rebecca Kocak;William Meeks;George Prousi;Patrick Anthony Xavier Hall
  • 通讯作者:
    Patrick Anthony Xavier Hall

William Meeks的其他文献

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{{ truncateString('William Meeks', 18)}}的其他基金

Research in the Geometry of Minimal and Constant Mean Curvature Surfaces
最小且恒定平均曲率曲面的几何研究
  • 批准号:
    1309236
  • 财政年份:
    2013
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Standard Grant
Research in the Geometry of Minimal and Constant Mean Curvature Surfaces
最小且恒定平均曲率曲面的几何研究
  • 批准号:
    1004003
  • 财政年份:
    2010
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Standard Grant
Research in Classical Minimal Surface Theory
经典极小曲面理论研究
  • 批准号:
    0703213
  • 财政年份:
    2007
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Standard Grant
Research in Classical Minimal Surface Theory
经典极小曲面理论研究
  • 批准号:
    0405836
  • 财政年份:
    2004
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Standard Grant
Research in Differential Geometry and Topology
微分几何与拓扑研究
  • 批准号:
    0104044
  • 财政年份:
    2001
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Research in Differential Geometry and Topology
数学科学:微分几何和拓扑研究
  • 批准号:
    9505101
  • 财政年份:
    1995
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Research in Differential Geometry andTopology
数学科学:微分几何和拓扑学研究
  • 批准号:
    9204535
  • 财政年份:
    1992
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Research in Differential Geometry andTopology
数学科学:微分几何和拓扑学研究
  • 批准号:
    8900285
  • 财政年份:
    1989
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Research In Differential Geometry andTopology
数学科学:微分几何和拓扑学研究
  • 批准号:
    8611574
  • 财政年份:
    1986
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Geometric Surfaces in Riemannian 3-Manifolds
数学科学:黎曼 3 流形中的几何曲面
  • 批准号:
    8414330
  • 财政年份:
    1984
  • 资助金额:
    $ 7.83万
  • 项目类别:
    Continuing grant

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加拿大微分几何和拓扑研究主席
  • 批准号:
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