Jacob Sturm
Universitatis Iagellonicae Acta Mathematica, Volume 52, 2015, pp. 29-43
https://doi.org/10.4467/20843828AM.15.004.3730We consider the space KR(n, F) of Kähler–Ricci solitons on n-dimensional Fano manifolds with Futaki invariant bounded by F. We prove a partial C0 estimate for KR(n, F) as a generalization of the recent work of Donaldson-Sun for Fano Kähler–Einstein manifolds. In particular, any sequence in KR(n, F) has a convergent subsequence in the Gromov- Hausdorff topology to a Kähler–Ricci soliton on a Fano variety with log terminal singularities.