On a Sharp Inequality Relating Yamabe Invariants on a Poincare-Einstein Manifold
Xiaodong Wang, Zhixin Wang
TL;DR
This paper proves a sharp inequality relating Yamabe invariants on Poincare-Einstein manifolds without any restrictions, extending previous results that required specific conditions.
Contribution
The authors remove restrictions from a known sharp inequality relating Yamabe invariants on Poincare-Einstein manifolds, establishing it in full generality.
Findings
The inequality holds without restrictions.
Extension of previous results to all Poincare-Einstein manifolds.
Strengthened understanding of Yamabe invariants in geometric analysis.
Abstract
For a Poincare-Einstein manifold under certain restrictions, X. Chen, M. Lai and F. Wang proved a sharp inequality relating Yamabe invariants. We show that the inequality is true without any restriction.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations