A decade of metric geometry in the space of K\"ahler metrics

TL;DR

This paper surveys recent developments over the past decade in the metric geometry of the space of Kähler metrics, highlighting key results and open problems in the field.

Contribution

It provides a comprehensive overview of recent progress and open questions in the metric geometry of Kähler metrics over the last ten years.

Findings

Summarizes key developments in the metric geometry of Kähler metrics

Highlights open problems and future research directions

Emphasizes progress made in the last decade

Abstract

We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.