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arXiv · 2409.02232

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

Dylan Langharst·Michael Roysdon·Yiming Zhao
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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.

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Dylan Langharst, Michael Roysdon, Yiming Zhao. 2024-09-05. On the $m$th-order Affine Pólya-Szegö Principle. https://doi.org/10.1007/s12220-025-02039-8

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