A survey of key results and open problems in the metric geometry of the space of Kähler metrics over the last ten years.
Berndtsson, A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in K¨ ahler geometry
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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.