61 citations · 233 across the 26 of their papers we have counts for
37 papers
Complex Monge-Amp{è}re equations on Hermitian Manifolds: From bounded to smooth solutions
Papa Badiane, Chinh H. Lu, Ahmed Zeriahi
We study regularity of bounded weak solutions to complex Monge-Amp{è}re equations on compact Hermitian manifolds with right-hand side possibly decreasing in the unknown. Our proof…
Geometric smoothing by the Kähler-Ricci Flow
Eleonora Di Nezza, Vincent Guedj, Chinh Hoang Lu
We study the geometric regularization of a positive closed current by the (twisted) Kähler-Ricci flow on a compact Kähler manifold. We conjecture that the local Arnold multipliciti…
Kähler-Ricci Flow: from divisors to cusps
Eleonora Di Nezza, Vincent Guedj, Chinh H. Lu
We study the geometric regularization of positive closed currents by the Kähler-Ricci flow on compact Kähler manifolds. In a previous work of ours, it was shown that the Kähler-Ric…
Singular Calabi-Yau metrics
Eleonora Di Nezza, Chinh H. Lu
These are notes of lectures given by the first named author during the CIME Summer school Calabi-Yau varieties. We survey known results concerning the complex Monge-Ampère equation…
A new approach to the Monge-Ampère eigenvalue problem
Chinh H. Lu, Ahmed Zeriahi
We study the eigenvalue problem for the complex Monge-Ampère operator in bounded hyperconvex domains in $\C^n$, where the right-hand side is a non-pluripolar positive Borel measure…
Uniform estimates: from Yau to Kolodziej
Vincent Guedj, Chinh H. Lu
In this note we provide a new and efficient approach to uniform estimates for solutions to complex Monge-Ampere equations, as well as for solutions to geometric PDE's that satisfy…
On uniqueness of solutions to complex Monge-Ampère mean field equations
Chinh H. Lu, Trong-Thuc Phung
We establish the uniqueness of solutions to complex Monge-Ampère mean field equations when the temperature parameter is small. In the local setting of bounded hyperconvex domains,…
Volumes of Bott-Chern classes
Sébastien Boucksom, Vincent Guedj, Chinh H. Lu
We study the volumes of transcendental and possibly non-closed Bott-Chern -classes on an arbitrary compact complex manifold . We show that the latter belongs to the class…
Relative pluripotential theory on compact Kähler manifolds
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Given a compact Kähler manifold, we survey the study of complex Monge-Ampère type equations with prescribed singularity type, developed by the authors in a series of papers. In add…
Degenerate complex Hessian equations on compact Hermitian manifolds
Vincent Guedj, Chinh H. Lu
In this note we provide uniform a priori estimates for solutions to degenerate complex Hessian equations on compact hermitian manifolds. Our approach relies on the corresponding a…
Plurisigned hermitian metrics
Daniele Angella, Vincent Guedj, Chinh H. Lu
Let be a compact hermitian manifold of dimension . We study the asymptotic behavior of Monge-Ampère volumes , when varies in the set of h…
Geodesic distance and Monge-Ampère measures on contact sets
Eleonora Di Nezza, Chinh H. Lu
We prove a geodesic distance formula for quasi-psh functions with finite entropy, extending results by Chen and Darvas. We work with big and nef cohomology classes: a key result we…
Quasi-plurisubharmonic envelopes 3: Solving Monge-Ampère equations on hermitian manifolds
Vincent Guedj, Chinh H. Lu
We develop a new approach to -a priori estimates for degenerate complex Monge-Ampère equations on complex manifolds. It only relies on compactness and envelopes propert…
Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds
Vincent Guedj, Chinh H. Lu
We develop a new approach to -a priori estimates for degenerate complex Monge-Ampère equations on complex manifolds. It only relies on compactness and envelopes propert…
Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Ampère volumes
Vincent Guedj, Chinh H. Lu
In \cite{GL21a} we have developed a new approach to -a priori estimates for degenerate complex Monge-Ampère equations, when the reference form is closed. This simplifyi…
Finite entropy vs finite energy
Eleonora Di Nezza, Vincent Guedj, Chinh H. Lu
Probability measures with either finite Monge-Ampère energy or finite entropy have played a central role in recent developments in Kähler geometry. In this note we make a systemati…
Comparison of Monge-Ampère capacities
Chinh H. Lu
Let be a compact Kähler manifold. We prove that all Monge-Ampère capacities are comparable. Using this we give an alternative direct proof of the integration by parts formu…
Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds
Chinh H. Lu, Trong-Thuc Phung, Tât-Dat Tô
Let be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge-Ampère equations with right-hand side in , . Using this we pro…
Pluripotential solutions versus viscosity solutions to complex Monge-Amp{è}re flows
Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi
We compare various notions of weak subsolutions to degenerate complex Monge-Amp{è}re flows, showing that they all coincide. This allows us to show that the viscosity solution coinc…
Complex Hessian equations with prescribed singularity on compact Kähler manifolds
Chinh H. Lu, Van-Dong Nguyen
Let be a compact Kähler manifold of dimension and fix . We prove that the total mass of the complex Hessian measure of --subharmonic functions is n…
Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry
Tamás Darvas, Chinh H. Lu
We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature Kähler metrics. We carry this out by explori…
metric geometry of big and nef cohomology classes
Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold of dimension , and be a closed smooth real -form representing a big and nef cohomology class. We introduce a metric $d_p, p\g…
Pluripotential Theory and Convex Bodies: Large Deviation Principle
Turgay Bayraktar, Thomas Bloom, Norman Levenberg +1
We continue the study in a previous work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in . Our goal is t…
Log-concavity of volume and complex Monge-Ampère equations with prescribed singularity
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold. We prove the existence and uniqueness of solutions to complex Monge-Ampère equations with prescribed singularity type. Compared to previou…