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.
