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We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian potential and the initial Calabi energy is bounded by some constant.
T. Aubin, Équations diférentielles non linéaires et probléme de Yamabe concernant la courbure scalaire
1976
Earlier work this paper cites.
E. Calabi, Extremal Kähler metric
1982
Earlier work this paper cites.
J. Lee, T. Parker, The Yamabe problem
1987
Earlier work this paper cites.
C. LeBrun, M. Singer, Existence and deformation theory for scalar-flat Kähler metrics on compact complex surfaces
1993
Earlier work this paper cites.
C. LeBrun, S. R. Simanca, Extremal Kähler metrics and Complex Deformation Theory
1994
Earlier work this paper cites.
A. Futaki, T. Mabuchi, Bilinear forms and extremal Kähler vector fields associated with Kähler classes
1995
Earlier work this paper cites.
R. Hamilton, A compactness property for solutions of the Ricci flow,
1995
Earlier work this paper cites.
A. Hwang, On the Calabi energy of extremal Kähler metrics
1995
Earlier work this paper cites.
T. Aubin, Some nonlinear problems in Riemannian geometry. Springer Monographs in Mathematics
1998
Cited alongside, same era.
S. Simanca, Strongly extremal Kähler metrics
2000
Cited alongside, same era.
X.X. Chen, Calabi flow in Riemann surfaces revisited
2001
Cited alongside, same era.
T. Mabuchi, A theorem of Calabi-Matsushima’s type,
2002
Cited alongside, same era.
J. Fine, Constant scalar curvature Kähler metrics on fibred complex surfaces
2004
Cited alongside, same era.
S.K. Donaldson, Lower bounds on the Calabi functional
2005
Cited alongside, same era.
S.K. Donaldson, Interior estimates for solutions of Abreu’s equation
G. Tian, J. Viaclovsky, Moduli spaces of critical metrics in dimension four
2005
Later among the works it cites.
V. Apostolov, D. Calderbank, P. Gauduchon, Hamiltonian 2-forms in Kähler geometry. I. General theory
2006
Later among the works it cites.
C. Arezzo, F. Pacard, Blowing up and desingularizing constant scalar curvature Kähler manifolds
2006
Later among the works it cites.
X.X. Chen, W.Y. He, On the Calabi flow
2008
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X. X. Chen, C. LeBrun, and B. Weber, On Einstein Conformally Kähler Metrics
2008
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S.K. Donaldson, Extremal metrics on toric surfaces I
2008
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2005
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S. Simanca, Heat flows for extremal metrics
2005
Cited alongside, same era.
C. Arezzo, F. Pacard, M. Singer, Extremal metrics on blow ups
Cited in the paper.
X.X. Chen, W.Y. He, The Calabi flow on Kähler surface with bounded Sobolev constant—(I)
Cited in the paper.
Cited in the paper.
G. Tian, unpublished note
Cited in the paper.
B. Zhou, X.H. Zhu, Relative K K -stability and modified K K -energy on toric manifolds
2008
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X.X. Chen, Space of Kähler metrics III–On the lower bound of the Calabi energy and geodesic distance
2009
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