17 citations · 43 across the 13 of their papers we have counts for
14 papers
On the transcendental Yau-Tian-Donaldson Conjecture
Antonio Trusiani
We prove the (uniform) Yau-Tian-Donaldson Conjecture for transcendental Kähler classes in the case of trivial automorphisms. Indeed, we show the existence of Special Kähler Fujita…
Continuous solutions to the quaternionic Monge-Ampère equation on locally flat HKT manifolds
Giovanni Gentili, Antonio Trusiani, Luigi Vezzoni
We prove that on a compact locally flat HKT manifold the quaternionic Monge--Ampère equation always has a unique continuous solution. This provides new evidence for the Conjecture…
Weighted extremal Kähler metrics on resolutions of singularities
Sébastien Boucksom, Mattias Jonsson, Antonio Trusiani
Generalizing previous results of Arezzo-Pacard-Singer, Seyyedali-Székelyhidi and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manif…
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…
Singular cscK metrics on smoothable varieties
Chung-Ming Pan, Tat Dat Tô, Antonio Trusiani
We prove the lower semi-continuity of the coercivity threshold of Mabuchi functional along a degenerate family of normal compact Kähler varieties with klt singularities. Moreover,…
Entropy for Monge-Ampère Measures in the Prescribed Singularities Setting
Eleonora Di Nezza, Stefano Trapani, Antonio Trusiani
In this note, we generalize the notion of entropy for potentials in a relative full Monge-Ampère mass , for a model potential . We then investigate stabili…
Kähler-Einstein metrics with positive curvature near an isolated log terminal singularity
Vincent Guedj, Antonio Trusiani, Sébastien Boucksom
We analyze the existence of Kähler-Einstein metrics of positive curvature in the neighborhood of a germ of a log terminal singularity . This boils down to solve a Dirichlet…
Kähler-Einstein metrics on families of Fano varieties
Chung-Ming Pan, Antonio Trusiani
Given a one-parameter family of -Fano varieties such that the central fibre admits a unique Kähler-Einstein metric, we provide an analytic method to show that the neigh…
A relative Yau-Tian-Donaldson conjecture and stability thresholds
Antonio Trusiani
Generalizing Fujita-Odaka invariant, we define a function on a set of generalized -divisors over a smooth Fano variety. This allows us to provide a new characterizatio…
Quasi-monotone convergence of plurisubharmonic functions
Vincent Guedj, Antonio Trusiani
The complex Monge-Ampère operator has been defined for locally bounded plurisubharmonic functions by Bedford-Taylor in the 80's. This definition has been extended to compact comple…
Kähler-Einstein metrics with prescribed singularities on Fano manifolds
Antonio Trusiani
Given a Fano manifold we develop a variational approach to characterize analytically the existence of Kähler-Einstein metrics with prescribed singularities, assuming that t…
Continuity method with movable singularities for classical Monge-Ampère equations
Antonio Trusiani
On a compact Kähler manifold , we study the strong continuity of solutions with prescribed singularities of complex Monge-Ampère equations with integrable Lebesgue densities…
The strong topology of -plurisubharmonic functions
Antonio Trusiani
On compact Kähler manifold, given a model type envelope (i.e. a singularity type) we prove that the Monge-Ampère operator is an homeomorphism between the se…
metric geometry of potentials with prescribed singularities on compact Kähler manifolds
Antonio Trusiani
Given compact Kähler manifold and a model type envelope with non-zero mass, i.e. a fixed potential determing some singularities such t…