11 citations · 24 across the 14 of their papers we have counts for
17 papers
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…
Sum of Squares Conjecture: the Monomial Case in
Jennifer Brooks, Dusty Grundmeier
The goal of this article is to prove the Sum of Squares Conjecture for real polynomials on with diagonal coefficient matrix. This conjecture describes…
Rational sphere maps, linear programming, and compressed sensing
John P. D'Angelo, Dusty Grundmeier, Jiri Lebl
We develop a link between degree estimates for rational sphere maps and compressed sensing. We provide several new ideas and many examples, both old and new, that amplify connectio…
Projective-umbilic points of circular real hypersurfaces in
David E. Barrett, Dusty E. Grundmeier
We show that the boundary of any bounded strongly pseudoconvex complete circular domain in must contain points that are exceptionally tangent to a projective image of…
Sup-norm Estimates for in
Dusty Grundmeier, Lars Simon, Berit Stensønes
We develop a method for proving sup-norm and Hölder estimates for on wide class of finite type pseudoconvex domains in . A fundamental obstructi…
Invariant CR Mappings between Hyperquadrics
Dusty Grundmeier, Kemen Linsuain, Brendan Whitaker
We analyze a canonical construction of group-invariant CR Mappings between hyperquadrics due to D'Angelo. Given source hyperquadric of , we determine the signature of the t…
Sums of CR functions from competing CR structures
David E. Barrett, Dusty E. Grundmeier
In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pl…
Initial monomial invariants of holomorphic maps
Dusty Grundmeier, Jiri Lebl
We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial idea…
An Application of Macaulay's Estimate to CR Geometry
Dusty Grundmeier, Jennifer Halfpap
Several questions in CR geometry lead naturally to the study of bihomogeneous polynomials on $\C^n \times \C^n$ for which $r(z,\bar{z})\norm{z}^{2d}=\norm{h(z)}^2$ f…
Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics
Dusty Grundmeier, Jiri Lebl, Liz Vivas
Using Green's hyperplane restriction theorem, we prove that the rank of a Hermitian form on the space of holomorphic polynomials is bounded by a constant depending only on the maxi…
Bounding the rank of positive Hermitian forms and rigidity for CR mappings of hyperquadrics
Dusty Grundmeier, Jiri Lebl
This paper has been withdrawn as the proof of Lemma 4.1 is incomplete.
Signature Pairs for Group-Invariant Hermitian Polynomials
Dusty Grundmeier
We study the signature pair for certain group-invariant Hermitian polynomials arising in CR geometry. In particular, we determine the signature pair for the finite subgroups of $SU…