Calabi flow on toric varieties with bounded Sobolev constant, I

Hongnian 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 -