Calabi flow on toric varieties with bounded Sobolev constant, I

• Autorzy: Hongnian Huang
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2016
• Tom: 3
• Numer: 1

Daty

otrzymano

2016-04-24

zaakceptowano

2016-07-31

online

2016-08-12

Twórcy

autor

Hongnian Huang

• Department of Mathematics and Statistics, MSC01 1115, 1 University of New Mexico, Albuquerque, NM 87131

Identyfikatory

DOI

10.1515/coma-2016-0009