4 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 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-…
Quantizing Geodesics in Kähler and Sasaki Geometry
Gilles Courtois, Eleonora Di Nezza, Thomas Franzinetti
The space of Kähler potentials can be quantized through the classical Fubini-Study map, relating infinite-dimensional geometric structures to finite-dimensional symmetric spaces.…
Convexity of the Mabuchi functional in big cohomology classes
Eleonora Di Nezza, Stefano Trapani, Antonio Trusiani
We study the Mabuchi functional associated to a big cohomology class. We define an invariant associated to transcendental Fujita approximations, whose vanishing is related to the Y…