arXiv subjects

Dusty E. Grundmeier

Publications and source records attributed to Dusty E. Grundmeier.

4 recordsLinked to original sources

arXiv2025

Invariant polynomials, gaps, and sparseness

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 polynomials with non-negative coefficients that are constant on the appropriate line or hyperplane. Our result provides crucial information about gaps in the possible target dimensions for certain invariant polynomial sphere maps. We interpret our results in terms of sparseness for solutions of certain linear systems.

math.CV↗

arXiv2021

Sums of CR and projective dual CR functions

A smooth, strongly $\mathbb{C}$-convex, real hypersurface $S$ in $\mathbb{CP}^n$ admits a projective dual CR structure in addition to the standard CR structure. Given a smooth function $u$ on $S$, we provide characterizations for when $u$ can be decomposed as a sum of a CR function and a dual CR function. Following work of Lee on pluriharmonic boundary values, we provide a characterization using differential forms. We further provide a characterization using tangential vector fields in the style of Audibert and Bedford.

math.CV↗

arXiv2020

Projective-umbilic points of circular real hypersurfaces in $\mathbb C^2$

We show that the boundary of any bounded strongly pseudoconvex complete circular domain in $\mathbb C^2$ must contain points that are exceptionally tangent to a projective image of the unit sphere.

math.CV↗

arXiv2018

Sums of CR functions from competing CR structures

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 pluriharmonic boundary values. In the second scenario the structures are related by projective duality considerations. In both cases we provide explicit vector field-based characterizations for two-dimensional circular domains satisfying natural convexity conditions.

math.CV↗