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arXiv · 1609.02047

Existence of coupled K\"ahler-Einstein metrics using the continuity method

Vamsi Pritham Pingali
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Abstract

In this paper we prove the existence of coupled K\"ahler-Einstein metrics on complex manifolds whose canonical bundle is ample. These metrics were introduced and their existence in the said case was proven by Hultgren and Nystr\"om using calculus of variations. We prove the result using the method of continuity. In the process of proving estimates, akin to the usual K\"ahler-Einstein metrics, we reduce existence in the Fano case to a C^0 estimate.

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Vamsi Pritham Pingali. 2016-09-07. Existence of coupled K\"ahler-Einstein metrics using the continuity method. https://arxiv.org/abs/1609.02047

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