On the $m$th-order Affine Pólya-Szegö Principle

Abstract

An affine Pólya-Szegö principle for a family of affine energies, with equality condition characterization, is demonstrated. In particular, this recovers, as special cases, the $L^p$ affine Pólya-Szegö principles due to Cianchi, Lutwak, Yang and Zhang, and subsequently Haberl, Schuster and Xiao. Various applications of this new Pólya-Szegö principle are shown.

arXiv comment26 pages

References in corpus (5)

• Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality
• The sharp affine $L^2$ Sobolev trace inequality and variants
• From affine Poincaré inequalities to affine spectral inequalities
• Higher-Order Lp Isoperimetric and Sobolev Inequalities
• The Pólya-Szegő inequality for smoothing rearrangements