Adam's Inequality on the Hyperbolic space

TL;DR

This paper establishes Adam's Inequality in Hyperbolic space, analyzes the asymptotic behavior of Sobolev best constants, and discusses the solvability of Q curvature PDEs in this geometric setting.

Contribution

It introduces Adam's Inequality in Hyperbolic space and explores its implications for Sobolev constants and Q curvature PDEs, extending classical results to a non-Euclidean setting.

Findings

Adam's Inequality is established in Hyperbolic space.

Asymptotic behavior of Sobolev best constants is characterized.

Conditions for solvability of Q curvature PDEs are discussed.

Abstract

In this article we establish an Adam's Inequality in the Hyperbolic space. As an application we will also prove the asymptotic behaviour of the best constants in the Sobolev inequality and also discuss the solvability of Q curvature type PDE's in the Hyperbolic space.