On curvature pinching of conic 2-spheres

Abstract

We study metrics on conic 2-spheres when no Einstein metrics exist. In particular, when the curvature of a conic metric is positive, we obtain the best curvature pinching constant. We also show that when this best pinching constant is approached, the conic 2-sphere has an explicit Gromov-Hausdorff limit. This is a generalization of the previous results of Chen-Lin and Bartolucci for 2-spheres with one or two conic points.

arXiv comment19 pages, 0 figure. Revision to fix some argument and typos

References in corpus (2)

• The Ricci flow on the sphere with marked points
• Convergence of the conical Ricci flow on S2 to a soliton