Extremal Kähler metrics

Gábor Székelyhidi

Extremal Kähler metrics

Gábor Székelyhidi^*

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

This paper is a survey of some recent progress on the study of Calabi's extremal Kähler 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.

Original language	English (US)
Title of host publication	Invited Lectures
Editors	Sun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
Publisher	KYUNG MOON SA Co. Ltd.
Pages	1017-1032
Number of pages	16
ISBN (Electronic)	9788961058056
State	Published - 2014
Event	2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of Duration: Aug 13 2014 → Aug 21 2014

Publication series

Name	Proceeding of the International Congress of Mathematicans, ICM 2014
Volume	2

Conference

Conference	2014 International Congress of Mathematicans, ICM 2014
Country/Territory	Korea, Republic of
City	Seoul
Period	8/13/14 → 8/21/14

Funding

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.

Keywords

Extremal metrics
K-stability
Kähler-Einstein metrics

ASJC Scopus subject areas

General Mathematics

Cite this

@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",

}

TY - GEN

T1 - Extremal Kähler metrics

AU - Székelyhidi, Gábor

N1 - 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: © 2014 Proceeding of the International Congress of Mathematicans, ICM 2014. All rights reserved.

PY - 2014

Y1 - 2014

N2 - This paper is a survey of some recent progress on the study of Calabi's extremal Kähler 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.

AB - This paper is a survey of some recent progress on the study of Calabi's extremal Kähler 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.

KW - Extremal metrics

KW - K-stability

KW - Kähler-Einstein metrics

UR - http://www.scopus.com/inward/record.url?scp=84989877234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989877234&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84989877234

T3 - Proceeding of the International Congress of Mathematicans, ICM 2014

SP - 1017

EP - 1032

BT - Invited Lectures

A2 - Jang, Sun Young

A2 - Kim, Young Rock

A2 - Lee, Dae-Woong

A2 - Yie, Ikkwon

PB - KYUNG MOON SA Co. Ltd.

T2 - 2014 International Congress of Mathematicans, ICM 2014

Y2 - 13 August 2014 through 21 August 2014

ER -

Extremal Kähler metrics

Abstract

Publication series

Conference

Funding

Keywords

ASJC Scopus subject areas

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