A survey of key results and open problems in the metric geometry of the space of Kähler metrics over the last ten years.
Finski, Geometry at infinity of the space of K¨ ahler potentials and asymptotic properties of filtrations
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A decade of metric geometry in the space of K\"ahler metrics
A survey of key results and open problems in the metric geometry of the space of Kähler metrics over the last ten years.