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

Full article: Open problems in pluripotential theory Skip to Main Content Taylor and Francis
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We survey the metric aspects of the Strominger–Yau–Zaslow conjecture on the existence of
special Lagrangian fibrations on Calabi–Yau manifolds near the large complex structure …

We prove that the non-Kähler locus of a nef and big class on a compact complex manifold
bimeromorphic to a Kähler manifold equals its null locus. In particular this gives an analytic …

For a large class of maximally degenerate families of Calabi–Yau hypersurfaces of complex
projective space, we study non-Archimedean and tropical Monge–Ampère equations, taking …

In this note, we investigate some regularity aspects for solutions of degenerate complex
Monge–Ampère equations (DCMAE) on singular spaces. First, we study the Dirichlet …

We show that the volume of transcendental big $(1, 1) $-classes on compact K\" ahler
manifolds can be realized by convex bodies, thus answering questions of Lazarsfeld …

Let (V, ω) be a compact Kähler manifold such that V admits a cover by Zariski-open Stein
sets with the property that ω has a strictly plurisubharmonic exhaustive potential on each …

We produce special Lagrangian $ T^ n $-fibrations on the generic regions of some Calabi-
Yau hypersurfaces in the Fermat family $ X_s=\{Z_0\ldots Z_ {n+ 1}+ e^{-s}(Z_0^{n+ …

We introduce the trace operator for quasi-plurisubharmonic functions on compact K\" ahler
manifolds, allowing to study the singularities of such functions along submanifolds where …