A Sharp Inequality Relating Yamabe Invariants on Asymptotically Poincare-Einstein Manifolds with a Ricci Curvature Lower Bound

TL;DR

This paper establishes a precise inequality connecting the Yamabe invariants of an asymptotically Poincare-Einstein manifold and its boundary, under a Ricci curvature lower bound, advancing understanding in geometric analysis.

Contribution

It introduces a sharp inequality linking interior and boundary Yamabe invariants for manifolds with Ricci curvature bounds, extending previous geometric analysis results.

Findings

Proves a sharp inequality relating interior and boundary Yamabe invariants.

Establishes conditions under which the inequality becomes equality.

Provides new insights into the geometry of asymptotically Poincare-Einstein manifolds.

Abstract

For an asymptotically Poincare-Einstein manifold with a lower Ricci curvature bound, we establish a sharp inequality relating the type II Yamabe invariant of the interior and the Yamabe invariant of its conformal infinity