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Wu, Xiang; Li, Shougui

The Orlicz Brunn-Minkowski inequality for dual harmonic quermassintegrals. (English) Zbl 1499.52007

Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 4, 945-954 (2019).
Summary: Within the framework of Orlicz Brunn-Minkowski theory recently introduced by E. Lutwak et al. [Adv. Math. 223, No. 1, 220–242 (2010; Zbl 1437.52006); J. Differ. Geom. 84, No. 2, 365–387 (2010; Zbl 1206.49050)], R. J. Gardner et al. [J. Eur. Math. Soc. (JEMS) 15, No. 6, 2297–2352 (2013; Zbl 1282.52006); J. Differ. Geom. 97, No. 3, 427–476 (2014; Zbl 1303.52002)], the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.

MSC:

52A39 Mixed volumes and related topics in convex geometry
52A40 Inequalities and extremum problems involving convexity in convex geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)

Keywords:

star body; dual harmonic quermassintegrals; Orlicz Brunn-Minkowski inequality

Citations:

Zbl 1437.52006; Zbl 1206.49050; Zbl 1282.52006; Zbl 1303.52002
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Full Text: DOI

References:

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