Extremum Values of Asymmetric Lp-Difference Bodies for Quermassintegrals and Dual Quermassintegrals

2018 ◽  
Vol 23 (4) ◽  
pp. 283-288 ◽  
Author(s):  
Wei Shi ◽  
Weidong Wang
Keyword(s):  
Dual Quermassintegrals

scholarly journals Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms

2020 ◽  
Vol 18 (1) ◽  
pp. 1064-1075
Author(s):  
Xia Zhao ◽  
Weidong Wang ◽  
Youjiang Lin
Keyword(s):  
Negative Answer ◽  
Positive Form ◽  
Dual Quermassintegrals ◽  
Monotonic Inequality ◽  
Star Bodies

Abstract In 2006, Schuster introduced the radial Blaschke-Minkowski homomorphisms. In this article, associating with the star duality of star bodies and dual quermassintegrals, we establish Brunn-Minkowski inequalities and monotonic inequality for the radial Blaschke-Minkowski homomorphisms. In addition, we consider its Shephard-type problems and give a positive form and a negative answer, respectively.

Quotient functions of dual quermassintegrals

2015 ◽  
Vol 38 (2) ◽  
pp. 271-283
Author(s):  
Chang-Jian Zhao
Keyword(s):  
Dual Quermassintegrals

CHORD POWER INTEGRALS OF SIMPLICES

2009 ◽  
Vol 02 (04) ◽  
pp. 557-565
Author(s):  
Wing-Sum Cheung ◽  
Ge Xiong
Keyword(s):  
Type Inequality ◽  
Projection Body ◽  
Polar Projection ◽  
Difference Body ◽  
Dual Quermassintegrals

In this paper, we obtain a formula relating the chord power integrals of a simplex K and the dual quermassintegrals of its difference body DK. As interesting applications, we express the volumes of difference body DK and polar projection body Π*K in terms of the volume of simplex K. Santaló-type inequality for chord power integrals of simplex is also established.

scholarly journals BRUNN–MINKOWSKI TYPE INEQUALITIES FOR Lp MOMENT BODIES

2013 ◽  
Vol 55 (2) ◽  
pp. 391-398 ◽  
Author(s):  
BAOCHENG ZHU ◽  
NI LI ◽  
JIAZU ZHOU
Keyword(s):  
Isoperimetric Inequalities ◽  
Dual Quermassintegrals

AbstractAbout 15 years ago, Lutwak and Zhang (E. Lutwak and G. Zhang, Blaschke–Santalo inequalities, J. Differ. Geom. 47 (1997), 1–16) introduced the notion of Lp moment bodies and established important volume inequalities for them, which were recently generalized by Haberl and Schuster (C. Haberl and E. Schuster, General Lp affine isoperimetric inequalities, J. Differ. Geom. 83 (2009), 1–26). In this paper, we establish new Brunn–Minkowski-type inequalities with respect to Blaschke Lp harmonic addition for the quermassintegrals and dual quermassintegrals of Lp moment bodies.

scholarly journals A characterization of dual quermassintegrals and the roots of dual Steiner polynomials

2018 ◽  
Vol 331 ◽  
pp. 565-588 ◽  
Author(s):  
David Alonso-Gutiérrez ◽  
Martin Henk ◽  
María A. Hernández Cifre
Keyword(s):  
Dual Quermassintegrals

scholarly journals On a question for dual quermassintegrals

2014 ◽  
pp. 1095-1103
Author(s):  
Chang-Jian Zhao ◽  
Xiao-Yan Li
Keyword(s):  
Dual Quermassintegrals
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