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This is a Quantitative Study study.

October 2, 2025Open Access

Dominating manifolds by radial spaces

Key Points

A Moser-Trudinger type inequality is validated using radial rearrangements on CD(k,n)-spaces, enabling broader applications.
The study characterizes manifolds that can admit Moser-Trudinger inequalities based on their Ricci curvature properties.
This work employs rearrangement techniques for functions to explore curvature-dimension inequalities in metric spaces.
Findings highlight the significance of curvature conditions in assessing the validity of certain inequalities on manifolds.

Abstract

This paper is devoted to a kind of rearrangement of functions on CD(k,n)-spaces, which satisfy a Polya-Szegö type inequality. We use this rearrangement to prove the validity of a Moser-Trudinger type inequality on a wide class of metric measure spaces satisfying a CD(k,n)-curvature-dimension inequality. As a consequence, we give a characterization, among manifolds with lower bounded Ricci curvature, of those admitting a Moser-Trudinger type inequality.

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Cite This Study

Samuel Bronstein (Wed,) studied this question.

synapsesocial.com/papers/68de5d9c83cbc991d0a203f2 https://doi.org/https://doi.org/10.48550/arxiv.2506.15621

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