On weighted extremal K\"ahler metrics
Abstract
The notion of weighted extremal K\"ahler metrics extends the classical notion of Calabi's extremal K\"ahler metrics, but includes many well-studied objects in K\"ahler geometry such as K\"ahler-Ricci solitons and Sasaki-Einstein metrics. In this paper, after explaining how this notion grew out, we will try to survey recent works concerning the YTD conjecture on weighted extremal K\"ahler metrics.
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