AbstractThe first non-round Einstein metrics on spheres were described in 1973 by Jensen in dimensions 4n+3 (n >0). For the next 25 years it remained an open problem whether the same could be done in even dimensions. This question was settled in 1998 when C. Böhm constructed infinite families of Einstein metrics on all Spheres of dimension between 5 and 9, in particular on $S^6$ and $S^8$. Over...
AbstractWe extend the notion of cscK metrics to singular varieties. We establish the existence of these canonical metrics on Q-Gorenstein smoothable klt varieties when the Mabuchi functional is coercive, these arise as a limit of cscK metrics on close-by fibres. The proof relies on developing a novel strong topology of pluripotential theory in families and establishing uniform estimates for csc...
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