Adams Inequality on Pinched Hadamard Manifolds

TL;DR

This paper establishes an Adams inequality for Sobolev spaces on Hadamard manifolds with specific curvature bounds, extending functional inequalities to non-compact negatively curved spaces.

Contribution

It proves a new Adams inequality for functions on Hadamard manifolds with curvature bounds, generalizing classical results to curved, non-compact settings.

Findings

Proved Adams inequality on Hadamard manifolds with curvature bounds

Extended functional inequalities to negatively curved non-compact manifolds

Provided tools for analysis on curved geometric spaces

Abstract

In this article we prove the Adams type inequality for $W^{m,p}(M)$ functions, where $m$ is a positive integer less than n and $(M,g)$ is a Hadamard manifold with Ricci curvature bounded from below and sectional curvature bounded from above by a negative constant.