Diameter estimate for closed manifolds with positive scalar curvature
Differential Geometry
2023-07-19 v2
Abstract
For a simply connected closed Riemannian manifold with positive scalar curvature, we prove an upper diameter bound in terms of its scalar curvature integral, the Yamabe constant and the dimension of the manifold. When a manifold has a conformal immersion into a sphere, the dependency on the Yamabe constant is not necessary. The power of scalar curvature integral in these diameter estimates is sharp and it occurs at round spheres with canonical metric.
Keywords
Cite
@article{arxiv.2112.06167,
title = {Diameter estimate for closed manifolds with positive scalar curvature},
author = {Xuenan Fu and Jia-Yong Wu},
journal= {arXiv preprint arXiv:2112.06167},
year = {2023}
}
Comments
Remark 1.2 and reference [2] added