Resumen de Valuations and Busemann�Petty type problems

Franz E. Schuster

• Projection and intersection bodies define continuous and GL(n) contravariant valuations. They played a critical role in the solution of the Shephard problem for projections of convex bodies and its dual version for sections, the Busemann�Petty problem. We consider the question whether FKFL implies V(K)V(L), where F is a homogeneous, continuous operator on convex or star bodies which is an SO(n) equivariant valuation. Important previous results for projection and intersection bodies are extended to a large class of valuations