Uniqueness of Kähler-Einstein cone metrics (Q1595453)

Let \(M\) be a compact complex manifold of complex dimension two or greater, and \(D\) a divisor with one irreducible component such that the co-homology class \(C_1(K_M)+\alpha C_1(O(D))\) for \(\alpha\in (0,1)\) contains a positive representative where \(K_M\) denotes the canonical bundle of \(M\) and \(O(D)\) the line bundle associated to \(D\). The author constructs an initial Kähler cone metric \(\omega\) with cone angle \(\alpha\) which is incomplete along divisor. It is proved also a type of maximum principle by showing that Kähler-Einstein metrics are unique in geometric Hölder spaces.