A survey of key results and open problems in the metric geometry of the space of Kähler metrics over the last ten years.
Finski, Small eigenvalues of Toeplitz operators, Lebesgue envelopes and Mabuchi 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.