Hermitian curvature flow

Jeffrey Streets; Gang Tian

Journal of the European Mathematical Society (2011)

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

Abstract

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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.

How to cite

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Streets, 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 -

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