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
• 负责人: Mu-Tao Wang
• 金额: $ 20.84万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605115&HistoricalAwards=false
• 关键词: Geometry; PDE; submanifolds; higher; codimensions

Professor Mu-Tao Wang proposes to study the geometry of higher codimensional submanifolds and the associated PDEs. He plans to continue his research on the mean curvature flow of Lagrangian submanifolds of Kahler-Einstein manifolds. This is closely related to a conjecture on the existence of special Lagrangians in Calabi-Yau manifolds. Professor Wang shall also continue his joint research project with Professor Shing-Tung Yau on the quasi-local mass of surfaces in general relativity. Immediate goals include understanding the conservation of the quasi-local mass and identifying the contribution of momentum.Professor Mu-Tao Wang purposes to study the geometry and PDEs associated with special curved geometric shapes, including special Lagrangians which are higher dimensional analogues of soap films and surfaces in space-time that are boundaries of space-like regions. The study of special Lagrangians will lead to the further understanding of the geometry of Calabi-Yau manifolds, the space of string theory. Professor Wang also plans to use the geometry and canonical PDEs on the boundary surfaces to detect the quasi-local energy-momentum contained in the space-like region. The proposed research will clarify the formation of black holes due to condensation of matter.

王木涛教授建议研究更高维子流形的几何结构和相关的偏微分方程。他计划继续研究卡勒-爱因斯坦流形的拉格朗日子流形的平均曲率流。这与卡拉比-丘流形中存在特殊拉格朗日量的猜想密切相关。王教授还将继续与丘成桐教授关于广义相对论中表面准局域质量的联合研究项目。 近期目标包括了解准局部质量守恒和确定动量的贡献。王木涛教授的目的是研究与特殊弯曲几何形状相关的几何和偏微分方程，包括特殊的拉格朗日量，它们是肥皂膜的高维类似物，时空中的表面是类空间区域的边界。对特殊拉格朗日量的研究将导致对卡拉比-丘流形几何、弦论空间的进一步理解。王教授还计划利用边界面上的几何和正则偏微分方程来检测类空间区域中包含的准局域能量动量。 拟议的研究将阐明由于物质凝聚而形成的黑洞。