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Uniqueness of conformal metrics with constant Q-curvature on closed Einstein manifolds

Jérôme Vétois

Abstract

On a smooth, closed Riemannian manifold $(M,g)$ of dimension $n\ge3$ with positive scalar curvature and not conformally diffeomorphic to the standard sphere, we prove that the only conformal metrics to $g$ with constant Q-curvature of order 4 are the metrics $λg$ with $λ>0$ constant.

Uniqueness of conformal metrics with constant Q-curvature on closed Einstein manifolds

Abstract

On a smooth, closed Riemannian manifold of dimension with positive scalar curvature and not conformally diffeomorphic to the standard sphere, we prove that the only conformal metrics to with constant Q-curvature of order 4 are the metrics with constant.
Paper Structure (2 sections, 4 theorems, 41 equations)

This paper contains 2 sections, 4 theorems, 41 equations.

Table of Contents

  1. Introduction and main result
  2. Extended versions and proof of Theorem \ref{['Th1']}

Key Result

Theorem 1.1

Let $$M,g$$ be a smooth, closed Einstein manifold of dimension $n\ge3$ with positive scalar curvature and not conformally diffeomorphic to the standard sphere. Then the only conformal metrics to $g$ with constant $\mathop{\mathrm{Q}}\nolimits$-curvature are the metrics $\lambda g$ with $\lambda>0$ c

Theorems & Definitions (4)

  • Theorem 1.1
  • Theorem 2.1
  • Theorem 2.2
  • Theorem 2.3