Inequalities for dual quermassintegrals of the radial pth mean bodies
نویسندگان
چکیده
Gardner and Zhang defined the notion of radial pth mean body (p > –1) in the Euclidean space Rn. In this paper, we obtain inequalities for dual quermassintegrals of the radial pth mean bodies. Further, we establish dual quermassintegrals forms of the Zhang projection inequality and the Rogers-Shephard inequality, respectively. Finally, Shephard’s problem concerning the radial pth mean bodies is shown when p > 0. MSC: 52A40; 52A20
منابع مشابه
On Inequalities for Quermassintegrals and Dual Quermassintegrals of Difference Bodies
In this paper, inequalities for quermassintegrals and dual quermassintegrals of difference bodies are given. In particular, an extension of the Rogers-Shephard inequality is obtained. Mathematics subject classification (2010): 52A40, 52A20.
متن کاملInequalities on asymmetric Lp-harmonic radial bodies
Lutwak introduced the Lp-harmonic radial body of a star body. In this paper, we define the notion of asymmetric Lpharmonic radial bodies and study their properties. In particular, we obtain the extremum values of dual quermassintegrals and the volume of the polars of the asymmetric Lp-harmonic radial bodies, respectively. c ©2017 All rights reserved.
متن کاملInequalities for Dual Affine Quermassintegrals
The setting for this paper is n-dimensional Euclidean space Rn. Let n denote the set of convex bodies (compact, convex subsets with nonempty interiors) and n o denote the subset of n that consists of convex bodies with the origin in their interiors. Denote by voli(K | ξ) the i-dimensional volume of the orthogonal projection of K onto an idimensional subspace ξ ⊂Rn. Affine quermassintegrals are ...
متن کاملThe Dual Brunn-minkowski Theory for Bounded Borel Sets: Dual Affine Quermassintegrals and Inequalities
This paper develops a significant extension of E. Lutwak’s dual Brunn-Minkowski theory, originally applicable only to star-shaped sets, to the class of bounded Borel sets. The focus is on expressions and inequalities involving chord-power integrals, random simplex integrals, and dual affine quermassintegrals. New inequalities obtained include those of isoperimetric and Brunn-Minkowski type. A n...
متن کاملInequalities for dual quermassintegrals of mixed intersection bodies
In this paper, we first introduce a new concept of 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015