52 citations · 78 across the 7 of their papers we have counts for
6 papers · 1 filter
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…
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…