5 problems

Let $(X,L)$ be a polarised toric variety with moment polytope $P$. Let $S(\omega)$ be the scalar curvature of a Kähler metric $\omega\in c_1(L)$, let $\hat{S}$ be its average, and…

Let $L\to M$ be an ample holomorphic line bundle over a compact Kähler manifold of complex dimension $m$, let $P(M,L)$ denote the relevant space of Hermitian metrics, and let…

Let $(L,h)$ be a positive Hermitian line bundle over a compact Kähler manifold $M$ of complex dimension $m$, and let $\beta_2(m)$ be the universal coefficient multiplying the Calab…

Finite-energy non-Archimedean equality conjecture. Equality is obtained provided one includes finite-energy non-Archimedean metrics.

Donaldson's equality conjecture. Equality should hold in this lower bound when the supremum is taken over the space of test configurations.