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Kähler–Einstein metrics along the smooth continuity method

Abstract

We show that if a Fano manifold M is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then M admits a Kähler–Einstein metric. This is a strengthening of the solution of the Yau–Tian–Donaldson conjecture for Fano manifolds by Chen–Donaldson–Sun (Int Math Res Not (8):2119–2125, 2014), and can be used to obtain new examples of Kähler–Einstein manifolds. We also give analogous results for twisted Kähler–Einstein metrics and Kahler–Ricci solitons.

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Datar, V., Székelyhidi, G. Kähler–Einstein metrics along the smooth continuity method. Geom. Funct. Anal. 26, 975–1010 (2016). https://doi.org/10.1007/s00039-016-0377-4

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  • DOI: https://doi.org/10.1007/s00039-016-0377-4