The study of complex Monge–Ampere equations on compact Kähler manifolds is an
important part of the interface between complex analysis and differential geometry …

We show that degenerate complex Monge-Ampère equations in a big cohomology class of a
compact Kähler manifold can be solved using a variational method, without relying on Yau's …

Well-known conjectures of Tian predict that the existence of canonical Kähler metrics should
be equivalent to various notions of properness of Mabuchi's K-energy functional. First, we …

We prove the existence and uniqueness of Kähler–Einstein metrics on ℚ-Fano varieties with
log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional …

We introduce different Finsler metrics on the space of smooth Kähler potentials that will
induce a natural geometry on various finite energy classes E χ˜(X, ω). Motivated by …

Full article: Open problems in pluripotential theory Skip to Main Content Taylor and Francis
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Let L be a big line bundle on a compact complex manifold X. Given a non-pluripolar
compact subset K of X and a continuous Hermitian metric e− φ on L, we define the energy at …

Let X be a compact Kähler manifold. Given a big cohomology class {θ}, there is a natural
equivalence relation on the space of θ-psh functions giving rise to 𝒮⁢(X, θ), the space of …

We establish the monotonicity property for the mass of nonpluripolar products on compact
Kähler manifolds, and we initiate the study of complex Monge–Ampère-type equations with …

Let (X, ω) be a compact connected Kähler manifold and denote by (ℰ p, dp) the metric
completion of the space of Kähler potentials ℋ ω with respect to the L p–type path length …