Geometry and PDE of submanifolds of higher codimensions

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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.