Lars Simon

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20172023

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6 papers · 1 filter

math.CV2021

Homogeneous Plurisubharmonic Polynomials in Higher Dimensions

Lars Simon

We prove several results on homogeneous plurisubharmonic polynomials on $C^{n}$ , $n \in Z_{\geq 2}$ . Said results are relevant to the problem of constructing local bu…

math.CV2019

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

Dusty Grundmeier, Lars Simon, Berit Stensønes

We develop a method for proving sup-norm and Hölder estimates for $\partial$ on wide class of finite type pseudoconvex domains in $C^{n}$ . A fundamental obstructi…

math.CV2018

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

Lars Simon, Berit Stensønes

We construct a bounded domain $Ω$ in $C^{2}$ with boundary of class $C^{1, 1}$ , such that $Ω$ has a Stein neighborhood basis, but is not $s$ -H-convex for a…

math.CV2018

A Homogeneous Function Constant along the Leaves of a Foliation

Lars Simon

Given a smooth foliation by complex curves (locally around a point $x \in C^{2} ∖ {0}$ ) which is "compatible" with the foliation by spheres centered at the origin, we…

math.CV2018

A Parameter Version of Forstnerič's Splitting Lemma

Lars Simon

We construct solution operators to the $\partial$ -equation that depend continuously on the domain. This is applied to derive a parameter version of Forstnerič's splittin…

math.CV2017

On Newton Diagrams of Plurisubharmonic Polynomials

Lars Simon, Berit Stensønes

Each extreme edge of the Newton diagram of a plurisubharmonic polynomial on $C^{2}$ gives rise to a plurisubharmonic polynomial. It is tempting to believe that the union of…

Homogeneous Plurisubharmonic Polynomials in Higher Dimensions

Sup-norm Estimates for ∂ in C3

An Example on s-H-Convexity in C2

A Homogeneous Function Constant along the Leaves of a Foliation

A Parameter Version of Forstnerič's Splitting Lemma

On Newton Diagrams of Plurisubharmonic Polynomials

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

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