Calabi flow on toric varieties with bounded Sobolev constant, I

Abstract: Let (X, P) be a toric variety. In this note, we show that the C0-norm of the Calabi flow φ(t) on X is uniformly bounded in [0, T) if the Sobolev constant of φ(t) is uniformly bounded in [0, T). We also show that if (X, P) is uniform K-stable, then the modified Calabi flow converges exponentially fast to an extremal Kähler metric if the Ricci curvature and the Sobolev constant are uniformly bounded. At last, we discuss an extension of our results to a quasi-proper Kähler manifold.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Calabi flow on toric varieties with bounded Sobolev constant, I ; volume:3 ; number:1 ; year:2016 ; extent:11 ; Complex manifolds ; 3, Heft 1 (2016) (gesamt 11)

Contributors, Places and Time

• Creator: Huang, Hongnian

Further information

• DOI: 10.1515/coma-2016-0009
• URN: urn:nbn:de:101:1-2410281501309.708984216334
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:29 AM CEST