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arXiv · 2605.08796

On weighted extremal K\"ahler metrics

Akito Futaki
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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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Akito Futaki. 2026-05-09. On weighted extremal K\"ahler metrics. https://arxiv.org/abs/2605.08796

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