Rellich inequalities via Riccati pairs on model space forms

• DOI: 10.1016/j.jmaa.2023.127870
• Publication Date: 2023-10-18T15:58:07Z
• Authors: Sándor Kajántó
• Keywords: Convexity; Constant (computer programming)

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 Kajántó, Kristály, Peter, and Zhao, discussing Hardy inequalities using Riccati pairs.