Taiwanese Journal of Mathematics


Denghui Wu, Zhenhui Bu, and Tongyi Ma

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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.

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

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

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

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


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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