A transport inequality on the sphere obtained by mass transport

TL;DR

This paper establishes a transport inequality on the sphere using McCann's map, linking it to sharp spectral estimates and expanding the understanding of geometric inequalities on curved spaces.

Contribution

It introduces a new transport inequality on the sphere derived via mass transport methods, connecting geometric curvature with spectral properties.

Findings

Proves a transport inequality on the sphere with positive Ricci curvature.

Derives sharp spectral comparison estimates from the inequality.

Links mass transport techniques to spectral geometry.

Abstract

Using McCann's transportation map, we establish a transport inequality on compact manifolds with positive Ricci curvature. This inequality contains the sharp spectral comparison estimates.