On the relative capacity on almost complex surface

TL;DR

This paper develops pluripotential theory on almost complex surfaces, demonstrating that J-holomorphic curves and negligible sets are pluripolar, and establishing a Josefson's type theorem in this setting.

Contribution

It introduces pluripotential theory to almost complex surfaces and proves key properties like pluripolarity of J-holomorphic curves and a Josefson's theorem.

Findings

J-holomorphic curves are pluripolar

Negligible sets are pluripolar

Josefson's theorem holds on almost Stein surfaces

Abstract

We built the pluripotential theory on almost complex surfaces. Using Bedford-Taylor type relative capacities we prove among others that J-holomorphic curves as well as negligible sets are pluripolar and Josefson's type theorem on almost Stein surfaces.