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We analyze a canonical construction of group-invariant CR Mappings between hyperquadrics due to DAngelo. 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 extend combinatorial results proven by Loehr, Warrington, and Wilf on determinants of sparse circulant determinants. We apply these results to study CR mappings invariant under finite subgroups of $U(1,1)$.
We summarize some work on CR mappings invariant under a subgroup of U(n) and prove a result on the failure of rigidity.
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an interesting result about inverse images.
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
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 decomp
We introduce several homotopy equivalence relations for proper holomorphic mappings between balls. We provide examples showing that the degree of a rational proper mapping between balls (in positive codimension) is not a homotopy invariant. In domain