Some generalized inequalities in Riemannian Geometry

TL;DR

This paper extends Hardy and Rellich-type inequalities on Riemannian manifolds, providing sharper estimates that account for the manifold's geometry, with new theorems and proofs.

Contribution

It introduces generalized inequalities in Riemannian geometry that incorporate weight functions and improve upon classical results with sharper estimates.

Findings

Extended Hardy and Rellich inequalities with weight functions

Derived new theorems and proofs in Riemannian geometry

Enhanced estimates considering manifold structure

Abstract

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical results by providing sharper estimates conforming the geometry and structure of the underlying manifold. We in this paper further extend the inequalities and in due course exhibit them in section [4] in terms of theorems and proofs.