A Caffarelli-Kohn-Nirenberg type inequality on Riemannian Manifolds

TL;DR

This paper extends the Caffarelli-Kohn-Nirenberg inequality to Riemannian manifolds using conformal Killing vector fields and Hardy inequality techniques.

Contribution

It introduces a novel generalization of a fundamental inequality to Riemannian geometry, broadening its applicability.

Findings

Established a generalized inequality on Riemannian manifolds.

Utilized conformal Killing vector fields in the proof.

Applied Hardy inequality methods to the geometric setting.

Abstract

We establish a generalization to Riemannian manifolds of the Caffarelli-Kohn-Nirenberg inequality. The applied method is based on the use of conformal Killing vector fields and Enzo Mitidieri's approach to Hardy inequalities.