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In this talk,I will report my recent joint work with Hao Fang on the best pinching constant on spheres with conic singularities.There are renewed interests in metrics with conic singularites after the seminal work of Troyanov.While on spheres and all cone angles are restricted to(0; 2π),necessary and suffcient conditions for the existence of constant positive curvature are obtained through works of Troyanov,Luo-Tian,Chen-Li.