Geometry and PDE of submanifolds of higher codimensions

王慕涛教授建议研究高次余维子流形的几何及其相关的偏微分方程组。他计划继续研究Kahler-Einstein流形的拉格朗日子流形的平均曲率流。这与关于Calabi-Yau流形中存在特殊拉格朗日的猜想密切相关。王教授亦会继续与邱成栋教授合作研究广义相对论中表面的准局部质量。近期目标包括了解准局部质量守恒和确定动量的贡献。王慕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组，包括特殊拉格朗日曲线，它是肥皂膜和时空表面的高维类似物，是类空间区域的边界。对特殊拉格朗日函数的研究将有助于进一步理解弦理论的空间--Calabi-Yau流形的几何性质。王教授还计划利用边界面上的几何和正则偏微分方程组来探测类空区域中包含的准局部能量动量。这项拟议的研究将阐明由于物质凝聚而形成的黑洞。

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.