The pseudo-Calabi flow
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Abstract
We define the pseudo-Calabi flow as
, ∆φf(φ) = S(ϕ) − S̲. Then we prove the well-posedness of this flow including the short time existence, the regularity of the solution and the continuous dependence on the initial data. Next, we point out that the L∞ bound on Ricci curvature is an obstruction to the extension of the pseudo-Calabi flow. Finally, we show that if there is a constant scalar curvature Kähler metric ω in its Kähler class, then for any initial potential in a small C2, α neighborhood of this metric (defined in terms of the C2, α norm on the Kähler potential), the pseudo-Calabi flow must converge exponentially fast to a constant scalar curvature Kähler metric near ω within the same Kähler class.
©[2013] by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Potential automorphy for certain Galois representations to GL2n
- Ring completion of rig categories
- Géométrie birationnelle équivariante des grassmanniennes
- Uniformly effective boundedness of Shafarevich Conjecture-type
- On the Dirichlet problem for variational integrals in BV
- The pseudo-Calabi flow
Articles in the same Issue
- Potential automorphy for certain Galois representations to GL2n
- Ring completion of rig categories
- Géométrie birationnelle équivariante des grassmanniennes
- Uniformly effective boundedness of Shafarevich Conjecture-type
- On the Dirichlet problem for variational integrals in BV
- The pseudo-Calabi flow
