Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Grundmeier, Dusty"'
Autor:
Grundmeier, Dusty, Lebl, Jiří
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 form for rational maps of balls. Using this normal form, we also provide
Externí odkaz:
http://arxiv.org/abs/2402.03152
Autor:
Brooks, Jennifer, Curry, Sean, Grundmeier, Dusty, Gupta, Purvi, Kunz, Valentin, Malcom, Alekzander, Palencia, Kevin
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 a canonical group-invariant CR mapping to obtain new invariant mapping
Externí odkaz:
http://arxiv.org/abs/2203.03494
We study real bihomogeneous polynomials $r(z,\bar{z})$ in $n$ complex variables for which $r(z,\bar{z}) \|z\|^2$ is the squared norm of a holomorphic polynomial mapping. Such polynomials are the focus of the Sum of Squares Conjecture, which describes
Externí odkaz:
http://arxiv.org/abs/2111.03192
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 deco
Externí odkaz:
http://arxiv.org/abs/2109.01199
Autor:
Brooks, Jennifer, Grundmeier, Dusty
The goal of this article is to prove the Sum of Squares Conjecture for real polynomials $r(z,\bar{z})$ on $\mathbb{C}^3$ with diagonal coefficient matrix. This conjecture describes the possible values for the rank of $r(z,\bar{z}) \|z\|^2$ under the
Externí odkaz:
http://arxiv.org/abs/2107.14739
Publikováno v:
Complex Analysis and its Synergies, 6 (2020), no. 1, Paper No. 4
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 connections with linear programming. We close with a list of ten open problems.
Externí odkaz:
http://arxiv.org/abs/1911.05559
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.
Comment: Some additional material
Comment: Some additional material
Externí odkaz:
http://arxiv.org/abs/1909.09542
We develop a method for proving sup-norm and H\"older estimates for $\overline{\partial}$ on wide class of finite type pseudoconvex domains in $\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the possibility of singular comp
Externí odkaz:
http://arxiv.org/abs/1909.04080
We analyze a canonical construction of group-invariant CR Mappings between hyperquadrics due to D'Angelo. Given source hyperquadric of $Q(1,1)$, we determine the signature of the target hyperquadric for all finite subgroups of $SU(1,1)$. We also exte
Externí odkaz:
http://arxiv.org/abs/1811.04978
Publikováno v:
Pacific J. Math. 293 (2018) 257-275
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
Externí odkaz:
http://arxiv.org/abs/1609.09119