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.

王慕涛教授建议研究高余维子流形的几何和相关的偏微分方程。他计划继续他的研究平均曲率流动的拉格朗日子流形的卡勒-爱因斯坦流形。这是密切相关的猜想存在的特殊拉格朗日在卡-丘流形。王教授亦会继续与丘成桐教授就广义相对论中表面的准定域质量进行合作研究。 近期目标包括了解准定域质量守恒和确定动量的贡献。王慕涛教授的目标是研究与特殊弯曲几何形状相关的几何和偏微分方程，包括特殊拉格朗日量，这是时空中肥皂膜和表面的高维模拟，是类空间区域的边界。对特殊拉格朗日量的研究将有助于进一步理解弦理论空间卡-丘流形的几何。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。 这项拟议中的研究将澄清由于物质凝结而形成的黑洞。