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Units : Differential Geometry | ULB175
Extremal Kähler metrics, when they exist, are ''canonical'' representatives of their Kähler class. Their existence is conjecturaly equiavlent to the stability of the underlying polarised variety. Via quanitsation, there is a strong connection between extremal metrics and balanced projective embeddings. In addition to these aspects we also consider the production of extremal metrics via geometric analysis. One tool for this is the Calabi flow which attempts to deform a given Kähler metric to an extremal one. The quantization of this flow is balancing flow, a certain flow on the space of projective embeddings. We are intereseted in better understanding Calabi flow via the projective geometry of balancing flow.