@inproceedings{186cac64febc4d319360dfce1596facb,
title = "Extremal K{\"a}hler metrics",
abstract = "This paper is a survey of some recent progress on the study of Calabi's extremal K{\"a}hler metrics. We first discuss the Yau-Tian-Donaldson conjecture relating the existence of extremal metrics to an algebro-geometric stability notion and we give some example settings where this conjecture has been established. We then turn to the question of what one expects when no extremal metric exists.",
keywords = "Extremal metrics, K-stability, K{\"a}hler-Einstein metrics",
author = "G{\'a}bor Sz{\'e}kelyhidi",
note = "Funding Information: Acknowledgements. Over the years I have benefited from conversations about extremal metrics with many people. In particular I would like to thank Simon Donaldson, Duong Phong, Julius Ross, Jacopo Stoppa, Richard Thomas and Valentino Tosatti for many useful discussions. The work presented in this survey was partially supported by the NSF. Publisher Copyright: {\textcopyright} 2014 Proceeding of the International Congress of Mathematicans, ICM 2014. All rights reserved.; 2014 International Congress of Mathematicans, ICM 2014 ; Conference date: 13-08-2014 Through 21-08-2014",
year = "2014",
language = "English (US)",
series = "Proceeding of the International Congress of Mathematicans, ICM 2014",
publisher = "KYUNG MOON SA Co. Ltd.",
pages = "1017--1032",
editor = "Jang, {Sun Young} and Kim, {Young Rock} and Dae-Woong Lee and Ikkwon Yie",
booktitle = "Invited Lectures",
}