arXiv subjects
Publications and source records attributed to Hongnian Huang.
Inspired by recent work of S. K. Donaldson on constant scalar curvature metrics on toric complex surfaces, we study obstructions to the extension of the Calabi flow on a polarized toric variety. Under some technical assumptions, we prove that the Calabi flow can be extended for all time.
We prove that on a Kähler manifold admitting an extremal metric $ω$ and for any Kähler potential $φ_0$ close to $ω$, the Calabi flow starting at $φ_0$ exists for all time and the modified Calabi flow starting at $φ_0$ will always be close to $ω$. Furthermore, when the initial data is invariant under the maximal compact subgroup of the identity component of the reduced automorphism group, the modified Calabi flow converges to an extremal metric near $ω$ exponentially fast.