This thesis presents three papers dealing with questions in Kähler geometry. In the first paper we construct a transform, called the Chebyshev transform, which maps continuous hermitian metrics on a big line bundle to convex functions on the associated Okounkov body. We show that this generalizes the classical Legendre transform in convex and toric geometry, and also Chebyshev constants in pluripotential theory. Our main result is that the integral of the difference of two transforms over the Okounkov body is equal to the Monge-Ampère energy of the two metrics. The Monge-Ampère energy, sometimes also called the Aubin-Mabuchi energy or the Aubin-Yau functional, is a well-known functional in Kähler geometry; it is the primitive function to th...
AbstractThe global Okounkov body of a projective variety is a closed convex cone that encodes asympt...
We study general linear perturbations of a class of 4d real-dimensional hyperkähler manifolds obtain...
International audienceThe main goal of this article is to construct "arithmetic Okounkov bodies" for...
This thesis presents three papers dealing with questions in K\ue4hler geometry. In the first paper w...
Let $L$ be a big holomorphic line bundle on a compact complex manifold $X.$ We show how to associate...
We associate to a test configuration for a polarized variety a filtration of the section ring of the...
We establish the convexity of Mabuchi’s K-energy functional along weak geodesics in the space of K\u...
AbstractThis article contains a detailed study in the case of a toric variety of the geodesic rays ϕ...
Starting with the data of a curve of singularity types, we use the Legendre transform to construct w...
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on on...
Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positiv...
Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positiv...
We study sufficient conditions for the existence of flat subspaces in the space of continuous pluris...
Given a K\ue4hler manifold X with an ample line bundle L, we consider the metric space of finite ene...
The global Okounkov body of a projective variety is a closed convex cone that encodes asymptotic inf...
AbstractThe global Okounkov body of a projective variety is a closed convex cone that encodes asympt...
We study general linear perturbations of a class of 4d real-dimensional hyperkähler manifolds obtain...
International audienceThe main goal of this article is to construct "arithmetic Okounkov bodies" for...
This thesis presents three papers dealing with questions in K\ue4hler geometry. In the first paper w...
Let $L$ be a big holomorphic line bundle on a compact complex manifold $X.$ We show how to associate...
We associate to a test configuration for a polarized variety a filtration of the section ring of the...
We establish the convexity of Mabuchi’s K-energy functional along weak geodesics in the space of K\u...
AbstractThis article contains a detailed study in the case of a toric variety of the geodesic rays ϕ...
Starting with the data of a curve of singularity types, we use the Legendre transform to construct w...
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on on...
Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positiv...
Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positiv...
We study sufficient conditions for the existence of flat subspaces in the space of continuous pluris...
Given a K\ue4hler manifold X with an ample line bundle L, we consider the metric space of finite ene...
The global Okounkov body of a projective variety is a closed convex cone that encodes asymptotic inf...
AbstractThe global Okounkov body of a projective variety is a closed convex cone that encodes asympt...
We study general linear perturbations of a class of 4d real-dimensional hyperkähler manifolds obtain...
International audienceThe main goal of this article is to construct "arithmetic Okounkov bodies" for...