31 citations · 268 across the 45 of their papers we have counts for
36 papers · 1 filter
Degree-Three Rational Sphere Maps: Sharp Denominator Region and Gram Normal Forms
Eden Danielsen-Jensen, Dusty Grundmeier, Abdullah Al Helal +4
We study degree-three rational sphere maps in two complex variables. After a standard normalization, the denominator of such a map takes the form \[ g_σ(z)=1+σ_1 z_1^2+σ_2 z_2^2, \…
CR functions at CR singularities: approximation, extension, and hulls
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
We study three possible definitions of the notion of CR functions at CR singular points, their extension to a fixed-neighborhood of the singular point, and analogues of the Baouend…
Rational Maps of Balls and their Associated Groups
Dusty Grundmeier, Jiří Lebl
Given a proper, rational map of balls, D'Angelo and Xiao introduced five natural groups encoding properties of the map. We study these groups using a recently discovered normal for…
On Segre-degenerate Levi-flat hypervarieties
Jiří Lebl, Luka Mernik
We prove that a singular real-analytic Levi-flat hypersurface in being Segre-degenerate at a point is equivalent to the existence of a so-called support curve…
Exhaustion functions and normal forms for proper maps of balls
Jiri Lebl
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putt…
Cartan uniqueness theorem on nonopen sets
Jiri Lebl, Alan Noell, Sivaguru Ravisankar
Cartan's uniqueness theorem does not hold in general for CR mappings, but it does hold under certain conditions guaranteeing extendibility of CR functions to a fixed neighborhood.…