Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Drnovšek, Barbara Drinovec"'
Given a bounded strictly convex domain $\Omega\Subset \mathbb{C}$ and a point $q\in \Omega$ we construct a continuous solution of the Pascali-type elliptic system of differential equations that is centered in $q$, maps the unit disc into $\Omega$ and
Externí odkaz:
http://arxiv.org/abs/2403.14170
Publikováno v:
J. Geom. Anal., 33:170, 2023
We show that if $E$ is a closed convex set in $\mathbb C^n$ $(n>1)$ contained in a closed halfspace $H$ such that $E\cap bH$ is nonempty and bounded, then the concave domain $\Omega = \mathbb C^n\setminus E$ contains images of proper holomorphic maps
Externí odkaz:
http://arxiv.org/abs/2301.01268
Publikováno v:
J. Math. Anal. Appl., 517(2):126653, 2023
In this paper we introduce and investigate a new notion of flexibility for domains in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ in terms of minimal surfaces which they contain. A domain $\Omega$ in $\mathbb R^n$ is said to be flexible if every conf
Externí odkaz:
http://arxiv.org/abs/2204.14254
Publikováno v:
Pure Appl. Math. Q. 19, No. 6, 2689-2735 (2023)
The second named author and David Kalaj introduced a pseudometric on any domain in the real Euclidean space $\mathbb R^n$, $n\ge 3$, defined in terms of conformal harmonic discs, by analogy with Kobayashi's pseudometric on complex manifolds, which is
Externí odkaz:
http://arxiv.org/abs/2109.06943
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.
Externí odkaz:
http://arxiv.org/abs/2104.03833
Publikováno v:
Complex Var. Elliptic Equ. 65 (2020), 489-497
Let D be a domain in C^n with smooth boundary, of finite 1-type at a point p in the boundary and such that the closure of D has a basis of Stein Runge neighborhoods. Assume that there exists an analytic disc which intersects the closure of D exactly
Externí odkaz:
http://arxiv.org/abs/1811.03363
Publikováno v:
Trans. Amer. Math. Soc. 371 (2019), no. 3, 1735-1770
In this paper, we prove that every conformal minimal immersion of a compact bordered Riemann surface $M$ into a minimally convex domain $D\subset \mathbb{R}^3$ can be approximated, uniformly on compacts in $\mathring M=M\setminus bM$, by proper compl
Externí odkaz:
http://arxiv.org/abs/1510.04006
Publikováno v:
Proc. London Math. Soc. (3) 111 (2015) 851-886
In this paper we find approximate solutions of certain Riemann-Hilbert boundary value problems for minimal surfaces in $\mathbb{R}^n$ and null holomorphic curves in $\mathbb{C}^n$ for any $n\ge 3$. With this tool in hand we construct complete conform
Externí odkaz:
http://arxiv.org/abs/1503.00775
Publikováno v:
Indag. Math. 27 (2016) 94-99
We prove that for any given upper semicontinuous function $\varphi$ on an open subset $E$ of $\mathbb C^n\setminus\{0\}$, such that the complex cone generated by $E$ minus the origin is connected, the homogeneous Siciak-Zaharyuta function with the we
Externí odkaz:
http://arxiv.org/abs/1501.07736
Autor:
Drnovsek, Barbara Drinovec
Publikováno v:
J. Math. Anal. Appl. 431 (2015) 705-713
We construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with $\mathcal{C}^2$-boundary in $\mathbb{C}^n$ into the unit ball of $\mathbb{C}^N$, for $N$ large enough, thereby answering a question of Alarcon and Forstne
Externí odkaz:
http://arxiv.org/abs/1501.00588