Hermitian curvature flow

• Autores: Jeffrey D. Streets, Gang Tian
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 13, Nº 3, 2011, págs. 601-634
• Idioma: inglés
• DOI: 10.4171/jems/262
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• Resumen

  • 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.