The areas log-Minkowski inequality. (English) Zbl 1467.52015
Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 115, No. 3, Paper No. 131, 10 p. (2021).
Summary: In this paper, we first propose and establish an Orlicz log-Minkowski inequality for affine surface areas by introducing new concepts of affine surface area measures and using the newly established Orlicz Minkowski inequality for mixed affine surface areas. The new Orlicz log-Minkowski inequality in special cases yields the classical Minkowski inequality for mixed affine surface areas, areas log-Minkowki inequality \(L_p\) log-Minkowski inequality for affine surface areas and other log-Minkowski type inequalities for affine surface areas.
MSC:
| 52A40 | Inequalities and extremum problems involving convexity in convex geometry |
| 52A39 | Mixed volumes and related topics in convex geometry |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
Keywords:
surface area; mixed surface area; \(L_p\)-mixed; Orlicz mixed surface area; log-Minkowski inequality; Orlicz Minkowski inequality for mixed surface areasReferences:
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