Bonnet-Myers type theorems for $Q$-curvature on four-manifolds

Mingxiang Li

Bonnet-Myers type theorems for $Q$-curvature on four-manifolds

Differential Geometry 2026-07-28 v1

Authors: Mingxiang Li

Abstract

Consider a complete four-dimensional Riemannian manifold $(M^4,g)$ whose scalar curvature $R_g$ is bounded below by a positive constant. First, if the Q-curvature $Q_g$ is also bounded below by a positive constant, then $M^4$ is compact. Second, if the quotient $Q_g/R_g$ bounded below by a positive constant $k$ , then the diameter of $M^4$ is less than or equal to $4\pi /\sqrt{15k}.$

Keywords

Q-curvature Bonnet-Myers theorem four-manifolds scalar curvature diameter bound compactness

Cite

@article{arxiv.2607.25343,
  title  = {Bonnet-Myers type theorems for $Q$-curvature on four-manifolds},
  author = {Mingxiang Li},
  journal= {arXiv preprint arXiv:2607.25343},
  year   = {2026}
}

Comments

13 pages