On the extension and smoothing of the Calabi flow on complex tori

DOI10.3934/dcds.2017265zbMath1372.53065arXiv1609.01834OpenAlexW2963269643MaRDI QIDQ2402888

Hongnian Huang

Publication date: 15 September 2017

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01834

zbMATH Keywords

Calabi flowcomplex toriextension and smoothing

Mathematics Subject Classification ID

Parabolic Monge-Ampère equations (35K96)

Cites Work

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• The global existence and convergence of the Calabi flow on \(\mathbb C^{n}/\mathbb Z^{n}+i \mathbb Z^{n}\)
• The Calabi flow on Kähler surfaces with bounded Sobolev constant. I
• On the extension of Calabi flow on toric varieties
• Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation
• Minimizing weak solutions for Calabi's extremal metrics on toric manifolds
• Extremal metrics on toric surfaces: a continuity method
• Extremal solitons and exponential \(C^\infty\) convergence of the modified Calabi flow on certain \(\mathbb C \text{P}^1\) bundles
• Constant scalar curvature metrics on toric surfaces
• Ricci deformation of the metric on complete non-compact Riemannian manifolds
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• The space of Kähler metrics.
• The space of Kähler metrics. II.
• Scalar curvature and stability of toric varieties.
• The long time behavior of fourth order curvature flows
• The Calabi flow on toric Fano surfaces
• Periodic solutions of Abreu's equation
• Long time existence of minimizing movement solutions of Calabi flow
• Interior estimates for solutions of Abreu equation
• The consistency and convergence of K-energy minimizing movements
• Existence of Einstein Metrics on Fano Manifolds
• Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics
• On the weak Kähler-Ricci flow
• On the Calabi flow
• The Calabi functional on a ruled surface
• Weakly Differentiable Functions
• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
• The affine Plateau problem
• Regularity of weak minimizers of the K-energy and applications to properness and K-stability