Henri Guenancia

activity

20102026

most citedKlt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups

47 citations · 143 across the 31 of their papers we have counts for

collaborators

Showing math.DGShow all

16 papers · 1 filter

math.DG2025

Kähler-Ricci flows coming out of metric spaces

Alix Deruelle, Vincent Guedj, Henri Guenancia +1

Given a compact Kähler manifold $X$ and a closed, positive $(1, 1)$ -current $T$ on $X$ , we find sufficient conditions for $T$ to induce a metric structure $(X, d_{T})$ which is the Gro…

math.DG2025

A note on orbifold regularity of canonical metrics

Henri Guenancia, Chung-Ming Pan, Mihai Păun

In this short note, we prove that on a compact Kähler variety $X$ with log terminal singularities and $c_{1} (X) = 0$ , any singular Ricci-flat Kähler metric has orbifold singularities i…

math.DG2025

Kähler-Einstein metrics of negative curvature

Henri Guenancia, Ursula Hamenstädt

Given any integer $n \geq 2$ , we construct a compact Kähler-Einstein manifold of dimension n of negative sectional curvature which is not covered by the ball.

math.DG2024

Degenerating conic Kähler-Einstein metrics to the normal cone

Olivier Biquard, Henri Guenancia

Let $X$ be a Fano manifold of dimension at least $2$ and $D$ be a smooth divisor in a multiple of the anticanonical class, $\frac{1}{α} (- K_{X})$ with $α > 1$ . It is well-known that Kähler-…

math.DG2023

Diameter of Kähler currents

Vincent Guedj, Henri Guenancia, Ahmed Zeriahi

We establish upper bounds on the diameter of compact Kähler manifolds endowed with Kähler metrics whose volume form satisfies an Orlicz integrability condition. Our results extend…

math.DG2023

Geometry of $K$ -trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures

Indranil Biswas, Junyan Cao, Sorin Dumitrescu +1

Let $X$ be a compact complex manifold such that its canonical bundle $K_{X}$ is numerically trivial. Assume additionally that $X$ is Moishezon or $X$ is Fujiki with dimension at most…

math.DG2021★ 7 cited

Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric

Olivier Biquard, Henri Guenancia

Let $X$ be a complex projective manifold and let $D \subset X$ be a smooth divisor. In this article, we are interested in studying limits when $β \to 0$ of Kähler-Einstein metrics $ω…

math.DG2019★ 2 cited

Variation of singular Kähler-Einstein metrics: Kodaira dimension zero

Junyan Cao, Henri Guenancia, Mihai Păun

We study several questions involving relative Ricci-flat Kähler metrics for families of log Calabi-Yau manifolds. Our main result states that if $p : (X, B) \to Y$ is a Kähler fiber sp…

math.DG2019

A Bochner principle and its applications to Fujiki class $C$ manifolds with vanishing first Chern class

Indranil Biswas, Sorin Dumitrescu, Henri Guenancia

We prove a Bochner type vanishing theorem for compact complex manifolds $Y$ in Fujiki class $C$ , with vanishing first Chern class, that admit a cohomology class $[α] \in H…

math.DG2018★ 1 cited

Quasi-projective manifolds with negative holomorphic sectional curvature

Henri Guenancia

Let $(M, ω)$ be a compact Kähler manifold with negative holomorphic sectional curvature. It was proved by Wu-Yau and Tosatti-Yang that $M$ is necessarily projective and has ample ca…

math.DG2017★ 5 cited

Variation of singular Kähler-Einstein metrics: positive Kodaira dimension

Junyan Cao, Henri Guenancia, Mihai Păun

Given a Kähler fiber space $p : X \to Y$ whose generic fiber is of general type, we prove that the fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on…

math.DG2016

Families of conic Kähler-Einstein metrics

Henri Guenancia

Let $p : X \to Y$ be an holomorphic surjective map between compact Kähler manifolds and let $D$ be an effective divisor on $X$ with generically simple normal crossings support and coe…

math.DG2015

Kähler-Einstein metrics: from cones to cusps

Henri Guenancia

In this note, we prove that on a compact Kähler manifold $X$ carrying a smooth divisor $D$ such that $K_{X} + D$ is ample, the Kähler-Einstein cusp metric is the limit (in a strong sen…

math.DG2015

Kähler-Einstein metrics with conic singularities along self-intersecting divisors

Henri Guenancia

In this paper, we extend the existence and regularity theorems for Kähler-Einstein metrics having conic singularities along a simple normal crossing divisor to the case of normal c…

math.DG2014★ 2 cited

On the boundary behavior of Kähler-Einstein metrics on log canonical pairs

Henri Guenancia, Damin Wu

In this paper, we study the boundary behavior of the negatively curved Kähler-Einstein metric attached to a log canonical pair $(X, D)$ such that $K_{X} + D$ is ample. In the case where…

math.DG2013★ 27 cited

Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors

Henri Guenancia, Mihai Păun

Let $X$ be a non-singular compact Kähler manifold, endowed with an effective divisor $D = \sum (1 - β_{k}) Y_{k}$ having simple normal crossing support, and satisfying $β_{k} \in (0, 1)$ . Th…

Kähler-Ricci flows coming out of metric spaces

A note on orbifold regularity of canonical metrics

Kähler-Einstein metrics of negative curvature

Degenerating conic Kähler-Einstein metrics to the normal cone

Diameter of Kähler currents

Geometry of K-trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures

Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric

Variation of singular Kähler-Einstein metrics: Kodaira dimension zero

A Bochner principle and its applications to Fujiki class C manifolds with vanishing first Chern class

Quasi-projective manifolds with negative holomorphic sectional curvature

Variation of singular Kähler-Einstein metrics: positive Kodaira dimension

Families of conic Kähler-Einstein metrics

Kähler-Einstein metrics: from cones to cusps

Kähler-Einstein metrics with conic singularities along self-intersecting divisors

On the boundary behavior of Kähler-Einstein metrics on log canonical pairs

Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors

Geometry of $K$ -trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures

A Bochner principle and its applications to Fujiki class $C$ manifolds with vanishing first Chern class