Orlicz–Lorentz centroid bodies
Copyright policy )Orlicz–Lorentz centroid bodies
We extend the definition of the centroid body operator to an Orlicz--Lorentz centroid body operator on the star bodies in $\mathbb R^n$, and establish the sharp affine isoperimetric inequality that bounds (from below) the volume of the Orlicz--Lorentz centroid body of any convex body containing the origin in its interior by the volume of this convex body.
22 pages, to appear in Advances in Applied Mathematics
Mathematics - Functional Analysis, affine isoperimetric inequalities, Steiner's symmetrization, Mathematics - Metric Geometry, Orlicz-Lorentz centroid body, Inequalities and extremum problems involving convexity in convex geometry, FOS: Mathematics, 52A40, Orlicz-Lorentz Busemann-Petty centroid inequality, Metric Geometry (math.MG), Functional Analysis (math.FA)
Mathematics - Functional Analysis, affine isoperimetric inequalities, Steiner's symmetrization, Mathematics - Metric Geometry, Orlicz-Lorentz centroid body, Inequalities and extremum problems involving convexity in convex geometry, FOS: Mathematics, 52A40, Orlicz-Lorentz Busemann-Petty centroid inequality, Metric Geometry (math.MG), Functional Analysis (math.FA)
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