Extreme properties of quermassintegrals of convex bodies

Gangsong Leng; Liansheng Zhang

doi:10.1007/BF02880133

Extreme properties of quermassintegrals of convex bodies

Gangsong Leng^*, Liansheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we establish two theorems for the quermassintegrals of convex bodies, which are the generalizations of the well-known Aleksandrov's projection theorem and Loomis-Whitney's inequality, respectively. Applying these two theorems, we obtain a number of inequalities for the volumes of projections of convex bodies. Besides, we introduce the concept of the perturbation element of a convex body, and prove an extreme property of it.

Original language	English
Pages (from-to)	837-845
Number of pages	9
Journal	Science in China, Series A: Mathematics
Volume	44
Issue number	7
DOIs	https://doi.org/10.1007/BF02880133
Publication status	Published - Jul 2001
Externally published	Yes

Keywords

Convex body
Mixed volume
Quermassintegral

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10.1007/BF02880133

Cite this

Leng, G., & Zhang, L. (2001). Extreme properties of quermassintegrals of convex bodies. Science in China, Series A: Mathematics, 44(7), 837-845. https://doi.org/10.1007/BF02880133

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AU - Leng, Gangsong

AU - Zhang, Liansheng

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AB - In this paper, we establish two theorems for the quermassintegrals of convex bodies, which are the generalizations of the well-known Aleksandrov's projection theorem and Loomis-Whitney's inequality, respectively. Applying these two theorems, we obtain a number of inequalities for the volumes of projections of convex bodies. Besides, we introduce the concept of the perturbation element of a convex body, and prove an extreme property of it.

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KW - Mixed volume

KW - Quermassintegral

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M3 - Article

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Extreme properties of quermassintegrals of convex bodies

Abstract

Keywords

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