题目：A theory of central measure for celestial mechanics
Abstract: Self-similar solutions for the n-body problem, whose configurations are called central configurations, are of special importance in celestial mechanics. Many mathematical tools have been applied to this ancient problem in the hope to understand their geometric properties, stability, finiteness, and the existence of certain classes of central configurations. In this talk we introduce a theory of central measures which generalizes central configurations to non-point masses and include continuum mass distributions. As an example, we show that if concentric spherical shells explode or collapse homothetically, then the ratio of outer and inner radii of adjacent shells is strictly between cubic root of 2 and infinity, and this bound is sharp.