# Hermitian curvature flow

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 3, page 601-634
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topStreets, Jeffrey, and Tian, Gang. "Hermitian curvature flow." Journal of the European Mathematical Society 013.3 (2011): 601-634. <http://eudml.org/doc/277526>.

@article{Streets2011,

abstract = {We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics with negative or zero first Chern class.},

author = {Streets, Jeffrey, Tian, Gang},

journal = {Journal of the European Mathematical Society},

keywords = {Chern connection; Euler-Lagrange equation; Kähler-Einstein metrics; Kähler-Einstein metrics; short time existence; Chern connection; Euler-Lagrange equation; Kähler-Einstein metrics; short time existence},

language = {eng},

number = {3},

pages = {601-634},

publisher = {European Mathematical Society Publishing House},

title = {Hermitian curvature flow},

url = {http://eudml.org/doc/277526},

volume = {013},

year = {2011},

}

TY - JOUR

AU - Streets, Jeffrey

AU - Tian, Gang

TI - Hermitian curvature flow

JO - Journal of the European Mathematical Society

PY - 2011

PB - European Mathematical Society Publishing House

VL - 013

IS - 3

SP - 601

EP - 634

AB - We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler–Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to Kähler–Einstein metrics, and are automatically Kähler–Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near Kähler–Einstein metrics with negative or zero first Chern class.

LA - eng

KW - Chern connection; Euler-Lagrange equation; Kähler-Einstein metrics; Kähler-Einstein metrics; short time existence; Chern connection; Euler-Lagrange equation; Kähler-Einstein metrics; short time existence

UR - http://eudml.org/doc/277526

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.