Orlicz mixed quermassintegrals. (English) Zbl 1328.52003
The authors extend the notion of mixed quermassintegrals from classical Brunn-Minkowski theory to Orlicz Brunn-Minkowski theory, calling it Orlicz mixed quermassintegrals. On that base they succeed to establish respective analogues of classical notions like Cauchy-Kubota formula, Minkowski’s isoperimetric inequality, the Brunn-Minkowski inequality, difference bodies and further ones. They also pose an interesting problem related to the conjectured log-Minkowski inequality.
Reviewer: Horst Martini (Chemnitz)
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:
Orlicz Brunn-Minkowski theory; quermassintegral; Minkowski’s isoperimetric inequality; integral geometryReferences:
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