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arXiv · 1511.02410

Generalized Matsushima's theorem and K\"ahler-Einstein cone metrics

Long Li·Kai Zheng
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Abstract

In this paper, we prove Matsushima's theorem for K\"ahler-Einstein metrics on a Fano manifold with cone singularities along a smooth divisor that is not necessarily proportional to the anti-canonical class. We then give an alternative proof of uniqueness of K\"ahler-Einstein cone metrics by the continuity method. Moreover, our method provides an existence theorem of K\"ahler-Einstein cone metrics with respect to conic Ding functional.

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Long Li, Kai Zheng. 2015-11-07. Generalized Matsushima's theorem and K\"ahler-Einstein cone metrics. https://doi.org/10.1007/s00526-018-1313-2

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