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On the uniqueness of Poincaré type cscK metrics
Let $X$ be a compact Kähler manifold with a divisor $D$ which may have simple normal crossings. We prove that the $K$-energy is convex on the space of Poincaré type Kähler metrics. Then, we prove that the Poincaré type constant scalar curvature Kähler metric is unique up to an automorphism of $X$ pr
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