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- W4287660462 abstract "We show the theorem which provides some sufficient condition to the non-existence of a complete Kahler--Einstein metric of negative scalar curvature whose holomorphic sectional curvature is negatively pinched: Let $Omega$ be a bounded weakly pseudoconvex domain in $mathbb{C}^n$ with a Kahler metric $omega$ whose holomorphic sectional curvature is negative near the topological boundary of $Omega$ (with respect to relative topology of $mathbb{C}^n$) and $omega$ admits the quasi-bounded geometry. Then $omega$ is uniformly equivalent to the Kobayashi--Royden metric and the following dichotomy holds: 1. $omega$ is complete, and $omega$ is uniformly equivalent to the complete Kahler--Einstein metric with negative scalar curvature. 2. $omega$ is incomplete, and there is no complete Kahler metric with negatively pinched holomorphic sectional curvature. Moreover, $Omega$ is Carath'eodory incomplete. Our approach is based on the construction of a Kahler metric of negatively pinched holomorphic sectional curvature and applying the implication of equivalence of invariant metrics inspired by Wu-Yau." @default.
- W4287660462 created "2022-07-25" @default.
- W4287660462 creator A5042976457 @default.
- W4287660462 date "2020-09-27" @default.
- W4287660462 modified "2023-10-17" @default.
- W4287660462 title "Non-existence of complete Kahler metric of negatively pinched holomorphic sectional curvature" @default.
- W4287660462 doi "https://doi.org/10.48550/arxiv.2009.13027" @default.
- W4287660462 hasPublicationYear "2020" @default.
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