par Pook, Julian 
Référence International mathematics research notices, 2016, 1, page (83-108)
Publication Publié, 2016
Référence International mathematics research notices, 2016, 1, page (83-108)
Publication Publié, 2016
Article révisé par les pairs
| Résumé : | We introduce a twisted version of the Calabi flow. Instead of constant scalar curvature Kähler (cscK) metrics, the twisted version of the Calabi flow is designed to find twisted constant scalar curvature Kähler metrics appearing in the works of Fine [7, 8], Song and Tian [10] and Stoppa [11]. For smooth initial data, we show that on compact Riemann surfaces of positive genus the twisted Calabi flow exists for all times and converges to a solution to the twisted constant scalar curvature Kähler equation under suitable convergence assumptions on the twisting 2-form. Key analytic ingredients are a priori bounds on twisted versions of the energy functionals used by Chruściel [5], Chen [3] and Struwe [13] in their treatment of the Calabi flow on Riemann surfaces. |
