Geodesic
Singular Kähler-Einstein metrics and RCD spaces
Forum of Mathematics, Pi, Tome 13 (2025) no. 1, p. e24

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We study Kähler-Einstein metrics on singular projective varieties. We show that under an approximation property with constant scalar curvature metrics, the metric completion of the smooth part is a noncollapsed RCD space, and is homeomorphic to the original variety. 
Szekelyhidi, Gabor. Singular Kähler-Einstein metrics and RCD spaces. Forum of Mathematics, Pi, Tome 13 (2025) no. 1, p. e24. doi: 10.1017/fmp.2025.10015
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