AbstractRecently, Dervan-Legendre considered the valuative criterion of polarized varieties. We will study the valuative stability and show that it is an open condition. We would like to study the valuative criterion for the Donaldson's J-equation. Motivated by the beta-invariant of Dervan-Legendre, we introduce a notion, the so-called valuative J-stability and prove that J-stability implies va...
AbstractEinstein metrics can be characterised as critical points of the (normalised) total scalar curvature functional. They are always saddle points. However, there are Einstein metrics which are local maxima of the functional restricted to metrics of fixed volume and constant scalar curvature. These are by definition stable Einstein metrics. Stability can equivalently be characterised by a sp...