Affine Orlicz P\'olya-Szeg\"o principles and their equality cases
Youjiang Lin, Dongmeng Xi
TL;DR
This paper proves a conjecture related to the affine Orlicz Pólya-Szegő principle and characterizes the conditions for equality in symmetrization cases, advancing the understanding of geometric inequalities.
Contribution
The paper confirms the conjecture about the affine Orlicz Pólya-Szegő principle and characterizes equality cases for Steiner and Schwarz symmetrizations.
Findings
Conjecture about the affine Orlicz Pólya-Szegő principle is proved.
Equality cases are characterized for Steiner and Schwarz symmetrizations.
Advances understanding of geometric inequalities in Orlicz spaces.
Abstract
The conjecture about the Orlicz P\'olya-Szeg\"o principle posed in [43] is proved. The cases of equality are characterized in the affine Orlicz P\'olya-Szeg\"o principle with respect to Steiner symmetrization and Schwarz spherical symmetrization.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology