L. Mernik

activity

20142023

most citedRegular versus singular order of contact on pseudoconvex hypersurfaces

7 citations · 13 across the 5 of their papers we have counts for

collaborators

5 papers

math.CV2023

On Segre-degenerate Levi-flat hypervarieties

Jiří Lebl, Luka Mernik

We prove that a singular real-analytic Levi-flat hypersurface $H$ in $C^{n}$ being Segre-degenerate at a point $p$ is equivalent to the existence of a so-called support curve…

math.CV2020

Plurisubharmonic Defining Functions in $C^{2}$

Luka Mernik

Let $Ω = {r < 0} \subset C^{2}$ , with $r$ plurisubharmonic on $b Ω = {r = 0}$ . Let $ρ$ be another defining function for $Ω$ . A formula for the determinant of the complex Hessian of…

math.CV2019★ 1 cited

Local Plurisubharmonic Defining Functions on the Boundary

Luka Mernik

Necessary conditions for a domain $Ω \subset C^{n}$ admitting a local plurisubharmonic defining function on the boundary are given. In tandem, we give an algorithm to construc…

math.CV2017★ 7 cited

Regular versus singular order of contact on pseudoconvex hypersurfaces

Jeffery D. McNeal, Luka Mernik

The singular and regular type of a point on a real hypersurface $H$ in $C^{n}$ are shown to agree when the regular type is strictly less than 4. If $H$ is p…

math.DS2014★ 5 cited

Central Strips of Sibling Leaves in Laminations of the Unit Disk

David J. Cosper, Jeffrey K. Houghton, John C. Mayer +2

Quadratic laminations of the unit disk were introduced by Thurston as a vehicle for understanding the (connected) Julia sets of quadratic polynomials and the parameter space of qua…