61 citations · 233 across the 26 of their papers we have counts for
16 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…
Quantization in geometric pluripotential theory
Tamás Darvas, Chinh H. Lu, Yanir A. Rubinstein
The space of Kähler metrics can, on the one hand, be approximated by subspaces of algebraic metrics, while, on the other hand, can be enlarged to finite-energy spaces arising in pl…
L^1 metric geometry of big cohomology classes
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Suppose is a compact Kähler manifold of dimension , and is closed -form representing a big cohomology class. We introduce a metric on the finite energy…
Monotonicity of non-pluripolar products and complex Monge-Ampère equations with prescribed singularity
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
We establish the monotonicity property for the mass of non-pluripolar products on compact Kahler manifolds, and we initiate the study of complex Monge-Ampere type equations with pr…
On the singularity type of full mass currents in big cohomology classes
Tamás Darvas, Eleonora Di Nezza, Chinh H. Lu
Let be a compact Kähler manifold and be a big cohomology class. We prove several results about the singularity type of full mass currents, answering a number of open qu…
From the Kähler-Ricci flow to moving free boundaries and shocks
Robert J. Berman, Chinh H. Lu
We show that the twisted Kähler-Ricci flow on a complex manifold X converges to a flow of moving free boundaries, in a certain scaling limit. This leads to a new phenomenon of sing…
Regularity of weak minimizers of the K-energy and applications to properness and K-stability
Robert J. Berman, Tamás Darvas, Chinh H. Lu
Let be a compact Kähler manifold and the space of Kähler metrics cohomologous to . If a cscK metric exists in , we show that all finite energy m…
Convexity of the extended K-energy and the large time behaviour of the weak Calabi flow
Robert J. Berman, Tamás Darvas, Chinh H. Lu
Let be a compact connected Kähler manifold and denote by the metric completion of the space of Kähler potentials with respect to the $L^…