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Berit Stensønes

Publications and source records attributed to Berit Stensønes.

5 recordsLinked to original sources
arXiv2020

Sup-norm Estimates for $\overline{\partial}$ in $\mathbb{C}^3$

We develop a method for proving sup-norm and Hölder estimates for $\overline{\partial}$ on wide class of finite type pseudoconvex domains in $\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the possibility of singular complex curves with exceptionally high order of contact with the boundary. Our method handles this problem, and in $\mathbb{C}^3$, we prove sup-norm and Hölder estimates for all bounded, pseudoconvex domains with real-analytic boundary.

math.CV↗
arXiv2019

Automorphisms of $\mathbb C^k$ with an invariant non-recurrent attracting Fatou component biholomorphic to $\mathbb C\times (\mathbb C^\ast)^{k-1}$

We prove the existence of automorphisms of $\mathbb C^k$, $k\ge 2$, having an invariant, non-recurrent Fatou component biholomorphic to $\mathbb C \times (\mathbb C^\ast)^{k-1}$ which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. Such a Fatou component also avoids $k$ analytic discs intersecting transversally at the fixed point. As a corollary, we obtain a Runge copy of $\mathbb C \times (\mathbb C^\ast)^{k-1}$ in $\mathbb C^k$.

math.CV↗
arXiv2018

An Example on $s$-H-Convexity in $\mathbb{C}^2$

We construct a bounded domain $Ω$ in $\mathbb{C}^2$ with boundary of class $\mathcal{C}^{1,1}$, such that $\overlineΩ$ has a Stein neighborhood basis, but is not $s$-H-convex for any real number $s\geq{1}$.

math.CV↗
arXiv2017

On Newton Diagrams of Plurisubharmonic Polynomials

Each extreme edge of the Newton diagram of a plurisubharmonic polynomial on $\mathbb{C}^2$ gives rise to a plurisubharmonic polynomial. It is tempting to believe that the union of the extreme edges or the convex hull of said union will do the same. We construct a plurisubharmonic polynomial $P$ on $\mathbb{C}^2$ with precisely two extreme edges $E_1$ and $E_2$, such that neither $E_1\cup{E_2}$ nor $\text{Conv}({E_1\cup{}E_2})$ yields a plurisubharmonic polynomial.

math.CV↗