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Title:
Calabi flow on admissible structures
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Abstract:
In this talk, we will discuss the Calabi flow on admissible structures defined by Apostolov, Calderbank, Gauduchon and Tonnesen-Friedman. The admissible structures can be seen as generalizations of toric varieties and Calabi's ansatz. We will show that on some admissible Kaehler manifolds, one can obtain the uniform C^0 norm of the Kaehler potentials of the Calabi flow by adapting the techniques developed in the study of the Calabi flow on toric manifolds with uniform Sobolev constant bounds. This ongoing research is motivated by the discussions with Vestislav Apostolov.
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