6 papers
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 multiplici…
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-…
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 equatio…
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 measur…
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…