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arXiv · 1711.09475

Invariant metrics on negatively pinched complete Kähler manifolds

Damin Wu·Shing-Tung Yau
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Abstract

We prove that a complete Kähler manifold with holomorphic curvature bounded between two negative constants admits a unique complete Kähler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly equivalent to the background Kähler metric. Furthermore, all three metrics are shown to be uniformly equivalent to the Bergman metric, if the complete Kähler manifold is simply-connected, with the sectional curvature bounded between two negative constants. In particular, we confirm two conjectures of R. E. Greene and H. Wu posted in 1979.

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Damin Wu, Shing-Tung Yau. 2017-11-26. Invariant metrics on negatively pinched complete Kähler manifolds. https://arxiv.org/abs/1711.09475

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