2 citations · 2 across the 6 of their papers we have counts for
12 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, \…
Invariant polynomials, gaps, and sparseness
John P. D'Angelo, Dusty E. Grundmeier, Daniel A. Lichtblau
We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polyn…
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…
Constructing Group-Invariant CR Mappings
Jennifer Brooks, Sean Curry, Dusty Grundmeier +4
We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D'Angelo's construction of…
Algebraic properties of Hermitian sums of squares, II
Jennifer Brooks, Dusty Grundmeier, Hal Schenck
We study real bihomogeneous polynomials in complex variables for which is the squared norm of a holomorphic polynomial mapping. Such polyn…
Sums of CR and projective dual CR functions
David E. Barrett, Dusty E. Grundmeier
A smooth, strongly -convex, real hypersurface in admits a projective dual CR structure in addition to the standard CR structure. Given a smooth func…