tailieunhanh - Báo cáo hóa học: "INEQUALITIES FOR DUAL AFFINE QUERMASSINTEGRALS"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: INEQUALITIES FOR DUAL AFFINE QUERMASSINTEGRALS | INEQUALITIES FOR DUAL AFFINE QUERMASSINTEGRALS YUAN JUN AND LENG GANGSONG Received 18 April 2005 Revised 2 November 2005 Accepted 8 November 2005 For star bodies the dual affine quermassintegrals were introduced and studied in several papers. The aim of this paper is to study them further. In this paper some inequalities for dual affine quermassintegrals are established such as the Minkowski inequality the dual Brunn-Minkowski inequality and the Blaschke-Santalo inequality. Copyright 2006 Y. Jun and L. Gangsong. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The setting for this paper is -dimensional Euclidean space R . Let 3 n denote the set of convex bodies compact convex subsets with nonempty interiors and 3Ỉ denote the subset of IK that consists of convex bodies with the origin in their interiors. Denote by vol K I ỉ the i-dimensional volume of the orthogonal projection of K onto an i-dimensional subspace ỉ c R . Affine quermassintegrals are important geometric invariants related to the projection of convex body. These quermassintegrals were introduced by Lutwak 7 and can be defined by letting ffi0 K V K ffi K k and for 0 i n ffii K k - r vol -i K I ỉ G -i k -i -1 d where the Grassmann manifold G i is endowed with the normalized Haar measure and k is the volume of the unit ball B in R . Furthermore in 6 Lutwak introduced the dual affine quermassintegrals of a star body L containing the origin in its interior t i L by letting t 0 L V L t L k and for 0 i 1 vol -i L nỉ ffi i L k dỉ G -i k -i Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID50181 Pages 1-7 DOI JIA 2006 50181 2 Inequalities for dual affine quermassintegrals where volz L n ỉ denotes the i-dimensional volume of intersection of L with an i-dimensional subspace ỉ c R