On Poletsky theory of discs in compact manifolds
We provide a direct construction of Poletsky discs via local arc approximation and a Runge-type theorem by A. Gournay.
math.CV↗
arXiv subjects
Uros Kuzman
Publications and source records attributed to Uros Kuzman.
Local approximation of non-holomorphic discs in almost complex manifolds
We provide a local approximation result of non-holomorphic discs with small d-bar by pseudoholomorphic ones. As an application, we provide a certain gluing construction.
math.CV↗
Gluing techniques and envelopes of disc functionals on almost complex manifolds
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.
math.CV↗
Lelong functional on almost complex manifolds
We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds.
math.CV↗