# Calabi flow on toric varieties with bounded Sobolev constant, I

Complex Manifolds (2016)

- Volume: 3, Issue: 1, page 211-221
- ISSN: 2300-7443

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topHongnian Huang. "Calabi flow on toric varieties with bounded Sobolev constant, I." Complex Manifolds 3.1 (2016): 211-221. <http://eudml.org/doc/285833>.

@article{HongnianHuang2016,

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.},

author = {Hongnian Huang},

journal = {Complex Manifolds},

keywords = {Kähler manifolds; toric varieties; Calabi flow},

language = {eng},

number = {1},

pages = {211-221},

title = {Calabi flow on toric varieties with bounded Sobolev constant, I},

url = {http://eudml.org/doc/285833},

volume = {3},

year = {2016},

}

TY - JOUR

AU - Hongnian Huang

TI - Calabi flow on toric varieties with bounded Sobolev constant, I

JO - Complex Manifolds

PY - 2016

VL - 3

IS - 1

SP - 211

EP - 221

AB - 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.

LA - eng

KW - Kähler manifolds; toric varieties; Calabi flow

UR - http://eudml.org/doc/285833

ER -

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