52 citations · 78 across the 7 of their papers we have counts for
11 papers
Infinite-dimensional flats in the space of positive metrics on an ample line bundle
Rémi Reboulet, David Witt Nyström
We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded fil…
The Minimum Principle for Convex Subequations
Julius Ross, David Witt Nyström
A subequation on an open subset is a subset of the space of -jets on with certain properties. A smooth function is said to be -subharmonic if a…
Coupled Kähler-Einstein metrics
Jakob Hultgren, David Witt Nyström
We propose new types of canonical metrics on Kähler manifolds, called coupled Kähler-Einstein metrics, generalizing Kähler-Einstein metrics. We prove existence and uniqueness resul…
Duality between the pseudoeffective and the movable cone on a projective manifold
David Witt Nyström, Sébastien Boucksom
We prove a conjecture of Boucksom-Demailly-Păun-Peternell, namely that on a projective manifold the cone of pseudoeffective classes in is dual to the…
Applications of the duality between the Complex Monge-Ampère Equation and the Hele-Shaw flow
Julius Ross, David Witt Nystrom
We give two applications of the the duality between the complex Homogeneous Monge-Ampère Equation (HMAE) and the Hele-Shaw flow. First, we prove existence of smooth boundary data f…
Harmonic Discs of Solutions to the Complex Homogeneous Monge-Ampère Equation
Julius Ross, David Witt Nyström
We study regularity properties of solutions to the Dirichlet problem for the complex Homogeneous Monge-Ampère equation. We show that for certain boundary data on the…
Homogeneous Monge-Ampère Equations and Canonical Tubular Neighbourhoods in Kähler Geometry
Julius Ross, David Witt Nyström
We prove the existence of canonical tubular neighbourhoods around complex submanifolds of Kähler manifolds that are adapted to both the holomorphic and symplectic structure. This i…
Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
Robert J. Berman, David Witt Nystrom
Let (X,L) be a (semi-) polarized complex projective variety and T a real torus acting holomorphically on X with moment polytope P. Given a probability density g on P we introduce a…
The Hele-Shaw flow and moduli of holomorphic discs
Julius Ross, David Witt Nystrom
We present a new connection between the Hele-Shaw flow, also known as two-dimensional (2D) Laplacian growth, and the theory of holomorphic discs with boundary contained in a totall…
Envelopes of positive metrics with prescribed singularities
Julius Ross, David Witt Nystrom
We investigate envelopes of positive metrics with a prescribed singularity type. First we generalise work of Berman to this setting, proving C^{1,1} regularity of such envelopes, s…
Analytic test configurations and geodesic rays
Julius Ross, David Witt Nystrom
Starting with the data of a curve of singularity types, we use the Legendre transform to construct weak geodesic rays in the space of locally bounded metrics on an ample line bundl…