Mabuchi K\"ahler solitons versus extremal K\"ahler metrics and beyond
Mabuchi K\"ahler solitons versus extremal K\"ahler metrics and beyond
Using the Yau-Tian-Donaldson type correspondence for $v$-solitons established by Han-Li, we show that a smooth complex $n$-dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal K\"ahler metric whose scalar curvature is strictly less than $2(n+1)$. Combined with previous observations by Mabuchi and Nakamura in the other direction, …