Related papers: Truncated tube domains with multi-sheeted envelope
After the investigation of the congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoscheme tilings \cite{SzJ1}, we consider the corresponding covering problems. In \cite{MSSz} the authors gave a partial…
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
We investigate the interrelation between topology and Narain T-duality of heterotic flux vacua. We present evidence that all 5 and 4-dimensional Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in the moduli space…
The H^2-regularity of variational solutions to a two-dimensional transmission problem with geometric constraint is investigated, in particular when part of the interface becomes part of the outer boundary of the domain due to the saturation…
We consider frequency-domain acoustic scattering at a homogeneous star-shaped penetrable obstacle, whose shape is uncertain and modelled via a radial spectral parameterization with random coefficients. Using recent results on the stability…
We determine all CR maps from the sphere in $\mathbb{C}^3$ into the tube over the future light cone in $\mathbb{C}^4$. This result leads to a complete characterization of proper holomorphic maps from the three-dimensional unit ball into the…
We show that the unit ball of a full Hilbert $C^*$-module is sequentially compact in a certain weak topology if and only if the underlying $C^*$-algebra is finite dimensional. This provides an answer to the question posed in J.…
The electronic spectrum of a two-dimensional square lattice in a perpendicular magnetic field has become known as the Hofstadter butterfly [Hofstadter, Phys. Rev. B 14, 2239 (1976).]. We have calculated quasi-one-dimensional analogs of the…
The authors showed in a preceding paper that in a connected locally harmonic manifold, the volume of a tube of small radius about a regularly parameterized simple arc depends only on the length of the arc and the radius. In this paper, we…
In this paper, the singular-value decomposition theory of complex matrices is explored to study constantly curved 2-spheres minimal in both $\mathbb{C}P^n$ and the hyperquadric of $\mathbb{C}P^n$. The moduli space of all those noncongruent…
Answering an old question, we find a domain X in the complex projective plane CP^2 which admits a strongly plurisubharmonic function, but such that every holomorphic function on X is constant. The domain X can be chosen diffeomorphic to an…
A question of F. Kwakkel and V. Markovic on existence of C^1-diffeomorphisms of closed surfaces that permute a dense collection of domains with bounded geometry is answered in the negative. In fact, it is proved that for closed surfaces of…
Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a cofinal family) in many separable metric spaces of interest. To get hold on uniform homotopy properties of these spaces, a reasonably behaved notion of an…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
This research announcement gives a brief report of the main results in our paper "PU(2) monopoles, I: Regularity, Uhlenbeck compactness, and transversality" (Journal of Differential Geometry, to appear). We describe the existence of…
The Hardy space on the unit ball in C^n provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n=1 the submodule has finite codimension. In this note…
Formation of domain walls during a rapid phase transition in a quasi one dimensional Cahn-Hiliard equation describing binary fluids in a thin tube is studied. Density of kinks scales like a sixth root of quench rate for equal concentrations…
The notion of a complex tangent arises for embeddings of real manifolds into complex spaces. It is of particular interest when studying embeddings of real $n$-dimensional manifolds into $\mathbb{C}^n$. The generic topological structure of…
The purpose of this article is towards systematically characterizing (holomorphic) retracts of domains of holomorphy; to begin with, bounded balanced pseudoconvex domains $B \subset \mathbb{C}^N$. Specifically, we show that every retract of…
Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube…