\(L_p\)-curvature measures and \(L_{p, q}\)-mixed volumes. (English) Zbl 1502.52009
\(L_p\)-curvature measure (as a generalization of the surface area measure) is introduced and studied. The associated \(L_{p,q}\)-mixed volume (which includes \(L_p\)-mixed volume as a special cases) is introduced. A Minkowski-type inequality related the \(L_{p,q}\)-mixed volume is proven, and the uniqueness of the solution for the corresponding Minkowski problem is obtained.
Reviewer: Gaiane Panina (Sankt-Peterburg)
MSC:
| 52A39 | Mixed volumes and related topics in convex geometry |
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