Taiwanese Journal of Mathematics

TWO COMPLEX COMBINATIONS AND COMPLEX INTERSECTION BODIES

Denghui Wu, Zhenhui Bu, and Tongyi Ma

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Abstract

This paper devotes to establish complex dual Brunn-Minkowski theory. At first, we introduce the concepts of complex radial combination and complex radial-Blaschke combination, and obtain the relations between those two combinations and dual mixed volumes. Then, we extend the properties of real intersection body to the complex case. Finally, we prove some complex geometric inequalities about complex intersection bodies and complex mixed intersection bodies, such as dual Brunn-Minkowski type, dual Aleksandrov-Fenchel type and dual Minkowski type inequality. Moreover, as applications, we get some corollaries including an isoperimetric type inequality and a uniqueness theorem.

Article information

Source
Taiwanese J. Math., Volume 18, Number 5 (2014), 1459-1480.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706521

Digital Object Identifier
doi:10.11650/tjm.18.2014.3904

Mathematical Reviews number (MathSciNet)
MR3265072

Zentralblatt MATH identifier
1357.52013

Subjects
Primary: 52A40: Inequalities and extremum problems 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]

Keywords
complex intersection bodies dual mixed volume complex radial-Blaschke combination dual Brunn-Minkowski type inequality

Citation

Wu, Denghui; Bu, Zhenhui; Ma, Tongyi. TWO COMPLEX COMBINATIONS AND COMPLEX INTERSECTION BODIES. Taiwanese J. Math. 18 (2014), no. 5, 1459--1480. doi:10.11650/tjm.18.2014.3904. https://projecteuclid.org/euclid.twjm/1499706521


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