Relative non-pluripolar product of currents

Monotonicity of Non-pluripolar Monge-ampère Masses

We prove that on a compact Kähler manifold, the non-pluripolar MongeAmpère mass of a θ-psh function decreases as the singularities increase. This was conjectured by Boucksom-Eyssidieux-Guedj-Zeriahi who proved it under the additional assumption of the functions having small unbounded locus. As a corollary we get a comparison principle for θ-psh functions, analogous to the comparison principle f...

Relative Currents

In this paper we define currents relative to a free factor system. We prove that a fully irreducible outer automorphism relative to a free factor system acts with uniform north-south dynamics on a subspace of the space of projective relative currents.

Relative Compactness and Product Stable Quotient Maps

Pluripolar Graphs Are Holomorphic

Let Ω be a domain in C and let f : Ω → C be a continuous function. We prove that the graph Γ(f) of the function f is a pluripolar subset of C if and only if f is holomorphic.

Relative non-Normal Graphs of a Subgroup of Finite Groups

Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or...