Mathematical Sciences: Minimal Surfaces and the Topology of 3-dimensional Manifolds

这个项目是关于技术的应用 微分几何的应用到三维空间的研究 流形 特别是，它旨在调查使用 极小曲面来研究非Haken三维流形及其 同构 它还旨在解决 三维流形的Heegaard分裂与调和 曲面的自同构。 关键是要自然但复杂 把三维物体切割成更简单的 通过最小面积的表面（如肥皂膜）来制造物体。 这已被证明是理解三维流形的一种有用的方法， 过去，而且可能会继续存在。

This project is concerned with applications of techniques of differential geometry to the study of 3-dimensional manifolds. In particular, it aims to investigate the use of minimal surfaces to study non-Haken 3-manifolds and their diffeomorphisms. It also aims to attack problems on the Heegaard splittings of 3-manifolds and on harmonic diffeomorphisms of surfaces. The point is to take natural but complicated three-dimensional objects and cut them apart into simpler objects by means of surfaces of least area (like soap films). This has proved a useful way to understand 3-manifolds in the past and will probably continue to be.