General Lp affine isoperimetric inequalities

Abstract

Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.

Cited by in corpus (25)

• The Logarithmic Minkowski Problem
• General affine surface areas
• Relative entropy of cone measures and $L_p$ centroid bodies
• The $L_p$-Minkowski problem for $-n<p<1$
• Anisotropic Fractional Sobolev Norms
• Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\varphi }$ affine and geominimal surface areas
• Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality
• New Orlicz Affine Isoperimetric Inequalities
• $L_p$ functional Busemann-Petty centroid inequality
• $L_p$ Minkowski Valuations on polytopes
• From affine Poincaré inequalities to affine spectral inequalities
• The Orlicz version of the $L_p$ Minkowski problem on $S^{n-1}$ for $-n<p<0$
• Convergence of symmetrization processes
• Rényi Divergence and $L_p$-affine surface area for convex bodies
• $\mathrm{SL}(\mathrm{n})$ covariant function-valued valuations
• Rearrangement and polarization
• On the discrete functional $l_p$ Minkowski problem
• Orlicz version of the mixed width integrals
• The dual Orlicz-Aleksandrov-Fenchel inequality
• Relative entropies for convex bodies
• Affine Orlicz Pólya-Szegö principles and their equality cases
• Constrained convex bodies with extremal affine surface areas
• $L_p$-Steiner quermassintegrals
• Orlicz hormonic Blaschke addition
• The Petty projection inequality for sets of finite perimeter