论文题目: Geodesics in the space of Kähler cone metrics, II. Uniqueness of constant scalar curvature Kähler cone metrics
论文作者: Kai Zheng
发表刊物: Communications on Pure and Applied Mathematics
In this article, we give a complete construction of geodesics in the space of Kähler cone metrics (cone geodesics) and we address the problem on the uniqueness of constant scalar curvature Kähler (cscK) cone metrics, when the cone angle stays in the whole interval (0,1). The part when the angle in [1/2,1) requires new weighted function spaces and new analytic techniques. We determine the asymptotic behaviour of both cone geodesics and cscK cone metrics, prove the reductivity of the automorphism group and establish the linear theory for the Lichnerowicz operator, which immediately implies the openness of the path deforming the cone angles of cscK cone metrics.