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.
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Acknowledgments
Both authors would like to thank Bartolucci for bringing up his work [1] to their attention.
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Communicated by C.S. Lin.
H. F.’s work is partially supported by NSF DMS-100829.
M. L.’s work is partially supported by Shanghai Sailing Program No. 15YF1406200 and NSFC No. 11501360.
