English

On weighted extremal K\"ahler metrics

Differential Geometry 2026-05-12 v1 Complex Variables

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.

Keywords

Cite

@article{arxiv.2605.08796,
  title  = {On weighted extremal K\"ahler metrics},
  author = {Akito Futaki},
  journal= {arXiv preprint arXiv:2605.08796},
  year   = {2026}
}

Comments

Submitted to the Proceedings of ICCM 2025