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The affine Pólya-Szegö principle: Equality cases and stability
1Institut für Diskrete Mathematik und Geometrie, TU Wien, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria.
Journal of Functional Analysis
|September 6, 2016
Summary
This study establishes a Brothers-Ziemer type theorem for the affine Pólya-Szegö principle. It also introduces and proves a quantitative version of this affine principle.
Area of Science:
- Mathematics
- Analysis
Background:
- The Pólya-Szegö principle relates to isoperimetric inequalities in analysis.
- Affine transformations are a key concept in geometry and linear algebra.
Purpose of the Study:
- To establish a Brothers-Ziemer type theorem for the affine Pólya-Szegö principle.
- To develop and prove a quantitative affine Pólya-Szegö principle.
Main Methods:
- Utilizing techniques from geometric analysis.
- Applying concepts from the theory of isoperimetric inequalities.
Main Results:
- A novel Brothers-Ziemer type theorem for the affine Pólya-Szegö principle has been established.
- A quantitative affine Pólya-Szegö principle has been successfully derived and proven.
Conclusions:
- The findings extend existing results in isoperimetric inequalities to the affine setting.
- The quantitative principle provides a new tool for analyzing geometric properties.
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