Generalized Hardy Type and Caffarelli-Kohn-Nirenberg Type Inequalities on Finsler Manifolds

TL;DR

This paper establishes generalized Hardy and Caffarelli-Kohn-Nirenberg inequalities on Finsler manifolds, revealing how manifold curvatures influence these geometric inequalities in both local and global contexts.

Contribution

It extends classical inequalities to Finsler manifolds, incorporating curvature effects and providing a unified geometric inequality framework.

Findings

Derived local and global inequalities on Finsler manifolds

Proved generalized Hardy and Caffarelli-Kohn-Nirenberg inequalities

Highlighted the influence of curvature on these inequalities

Abstract

In this paper we derive both local and global geometric inequalities on general Riemannnian and Finsler manifolds and prove generalized Caffarelli-Kohn-Nirenberg type and Hardy type inequalities on Finsler manifolds, illuminating curvatures of both Riemannian and Finsler manifolds influence geometric inequalities.