Dominating manifolds by radial spaces

2025/06/18 by Samuel Bronstein, Bronstein, Samuel
Mathematics · #46T12 #49Q99 #58J99 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2506.15621

openalex publication_date 2025/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Fine Pólya-Szegő rearrangement inequalities in metric spaces and applications
• Almost-fuchsian structures on disk bundles over a surface
• Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below
• Non-collapsed spaces with Ricci curvature bounded from below
• New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case
• On the differential structure of metric measure spaces and applications
• Trudinger-Moser inequalities on complete noncompact Riemannian manifolds
• Local Poincar 'e inequalities from stable curvature conditions on metric\n spaces
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Moser-Trudinger inequality on conformal discs
• Weak curvature conditions and functional inequalities
• Functions of bounded variation on “good” metric spaces
• On Imbeddings into Orlicz Spaces and Some Applications

Related

• A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space
• Trudinger-Moser embedding on the hyperbolic space
• New geometric aspects of Moser-Trudinger inequalities on Riemannian manifolds: the non-compact case
• Aubin type almost sharp Moser-Trudinger inequality revisited
• Moser-Trudinger inequality on conformal discs