arXiv subjects
Publications and source records attributed to Uroš Kuzman.
We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.
Given a bounded strictly convex domain $Ω\Subset \mathbb{C}$ and a point $q\in Ω$ we construct a continuous solution of the Pascali-type elliptic system of differential equations that is centered in $q$, maps the unit disc into $Ω$ and the unit circle into $\partial Ω$.
Based on Runge theorem for generalized analytic vectors proved by Goldschmidt in 1979 we provide a Mergelyan-type and a Carleman-type approximation theorems for solutions of Pascali systems.
We solve the non-linear Cousin problem for $J$-holomorphic maps. That is, we provide a gluing method for the pseudoholomorphic maps defined on a Cartan pair of domains in $\mathbb{C}$.
We prove that every $J$-holomorphic variational vector field can be realized as derivation $\frac{d}{dt}_{|t=0}f_t$ where $(f_t)$ is a one parametric family of $J$-holomorphic discs. Furthermore, we discuss properness of an extremal $J$-holomorphic disc in a bounded pseudoconvex domain.
We consider the dynamics of complex rational maps on the Riemann sphere. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini-Study distances between finitely many initial elements of the orbit and the origin, ergodic properties of the rational map are preserved.