On the best pinching constant of conformal metrics on S^2 with one and two conical singularities


We answer a long-standing open question asked by Thurston (The Geometry and Topology of Three-Manifolds. Princeton University Press, Princeton, 1978) concerning the best pinching constant for conformal metrics on S2 with one and two conical singularities of angles 2π(1+α 1) and 2π(1+α 1),2π(1+α 2) in case α 1∈(−1,0) and −1<α 1<α 2<0, respectively. The case of one conical singularity is a corollary of a result in Chen and Lin (Commun. Anal. Geom. 6(1):1–19, 1998) concerning the curvature of conformal metrics on ℝ2 with bounded Gaussian curvature 0<a≤K≤b<+∞. The case with two conical singularities is worked out by a generalization of that result

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oaioai:art.torvergata.it:2108/13671Last time updated on 3/29/2020

This paper was published in ART.

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