國立清華大學 數學系

Abstract:
In this talk, I will give a brief introduction to some basic results in classical integral geometry, focusing on various formulas for determining the volumes and surface areas of domains in n-dimensional Euclidean spaces. In particular, when the domains are convex, tools from convex geometry can be applied to study their geometric properties. Within this framework, I will introduce the Busemann–Petty problem, review its historical solutions, and discuss possible generalizations to other geometric spaces.