The Three-Body Problems and Global Differential Geometry of Submanifolds

小行星9705752 这个项目在于微分几何及其在力学中的应用。具体来说，研究人员是追求几何方法的三体问题，无论是在天体力学和量子力学。其思想是在给定力学系统的位形空间上引入一个自然度规，使得运动的动能由速度平方的一半给出;然后利用欧几里得对称群研究由此产生的运动学黎曼流形。此外，研究人员将继续他的工作，最小超曲面和等周区域。 经典的三体问题与理解三重质点在引力作用下的轨道结构有关。本计画的一个重要概念是以运动的动能为出发点来研究三体问题。极小超曲面是肥皂膜曲面的高维推广，它们满足显着的极值性质。

9705752 Hsiang This project lies in the area of differential geometry and its applications to mechanics. Specifically, the investigator is to pursue a geometric approach to the three body problems, both in celestial mechanics and in quantum mechanics. The idea is to introduce a natural metric on the configuration space of a given mechanical system such that the kinetic energy of a motion is given by half of the square of speed; one then studies the resulting kinematic riemannian manifold, making use of the Euclidean symmetry group. In addition, the investigator is to continue his work on minimal hypersurfaces and isoperimetric regions. The classical three body problem has to do with understanding the orbit structures of triples of mass points under gravity. A key idea in the current project is to study the three body problem with the kinetic energy of a motion as a starting point. Minimal hypersurfaces are higher dimensional generalizations of soap film surfaces; they satisfy remarkable extremal properties.