Hermitian curvature flow

Jeffrey Streets, Gang Tian

Research output: Contribution to journalArticle

48 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)601-634
Number of pages34
JournalJournal of the European Mathematical Society
Volume13
Issue number3
DOIs
StatePublished - Mar 7 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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