Rellich inequalities via Riccati pairs on model space forms

Abstract

We present a simple method for proving Rellich inequalities on Riemannian manifolds with constant, non-positive sectional curvature. The method is built upon simple convexity arguments, integration by parts, and the so-called Riccati pairs, which are based on the solvability of a Riccati-type ordinary differential inequality. These results can be viewed as the higher order counterparts of the recent work by Kaj\'ant\'o, Krist\'aly, Peter, and Zhao, discussing Hardy inequalities using Riccati pairs.