Valuations and Busemann�Petty type problems

• Autores: Franz E. Schuster
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 1, 2008, págs. 344-368
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.05.001
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• Resumen

  • 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