Gluing techniques and envelopes of disc functionals on almost complex manifolds

TL;DR

This paper extends the theory of plurisubharmonic envelopes of disc functionals to almost complex manifolds, generalizing previous results and providing applications in regularization and hull characterization.

Contribution

It generalizes plurisubharmonicity results for envelopes of Poisson and Lelong functionals to higher-dimensional almost complex manifolds.

Findings

Proves plurisubharmonicity of envelopes on almost complex manifolds.

Provides applications to regularization of J-plurisubharmonic functions.

Characterizes compact psh-hulls via pseudoholomorphic discs.

Abstract

We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We also provide some applications to the regularization of J-plurisubharmonic functions and to the characterization of compact psh-hulls by pseudoholomorphic discs.