47 citations · 143 across the 31 of their papers we have counts for
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Strict positivity of Kähler-Einstein currents
Vincent Guedj, Henri Guenancia, Ahmed Zeriahi
Kähler-Einstein currents, also known as singular Kähler-Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular co…
Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric
Junyan Cao, Henri Guenancia, Mihai Păun
In this note, we obtain various formulas for the curvature of the metric on the direct image of the relative canonical bundle twisted by a holomorphic line bundle endowed wit…
Continuity of singular Kähler-Einstein potentials
Vincent Guedj, Henri Guenancia, Ahmed Zeriahi
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 problem fo…
Families of singular Kähler-Einstein metrics
Eleonora Di Nezza, Vincent Guedj, Henri Guenancia
Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Ampère equations on compact Kähler manifolds, that allo…
Kähler-Einstein metrics on stable varieties and log canonical pairs
Robert J. Berman, Henri Guenancia
Let be a canonically polarized variety, i.e. a complex projective variety such that its canonical class defines an ample $\Q-$line bundle, and satisfying the conditions…
Kähler-Einstein metrics with cone singularities on klt pairs
Henri Guenancia
Let (X,D) be a klt pair. Assuming either K_X+D big or -(K_X+D) ample, and that the coefficients of D are greater than 1/2, we show that the Kähler-Einstein metric attached to (X,D)…
Kähler-Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor
Henri Guenancia
Let X be a Kähler manifold and D be a R-divisor with simple normal crossing support and coefficients between 1/2 and 1. Assuming that K_X+D is ample, we prove the existence and uni…
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
Frédéric Campana, Henri Guenancia, Mihai Păun
We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact Kähler manifold, under a t…
Toric plurisubharmonic functions and analytic adjoint ideal sheaves
Henri Guenancia
In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description…