Inequalities for dual quermassintegrals of mixed intersection bodies

2005/03/05 by Zhao Chang-jian, Leng Gang-song
Mathematics · #math.MG #msc:54A50

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 1, February 2005, pp. 79-91 · 13 pages

arxiv created 2005/03/05 · arxiv updated 2009/12/01

Abstract

In this paper, we first introduce a new concept of \it dual quermassintegral sum function of two star bodies and establish Minkowski's type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. Then, we give the Aleksandrov--Fenchel inequality and the Brunn--Minkowski inequality for mixed intersection bodies and some related results. Our results present, for intersection bodies, all dual inequalities for Lutwak's mixed prosection bodies inequalities.

Related

• The Minkowski problem based on the (p,q)-mixed quermassintegrals
• On \pmbp-quermassintegral differences function
• Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals
• Dual Brunn-Minkowski inequality for C-star bodies
• The mixed affine quermassintegrals