7 papers
Phase retrieval from a uniformly discrete point set
Jaume de Dios Pont, Josef Greilhuber, Lukas Liehr +1
We prove that for every window of the form , where is a polynomial, there exists a uniformly discrete set of points $\mathcal{S} \subset \mathbb R^…
Non-density of nodal lines in the clamped plate problem
Alberto Enciso, Josef Greilhuber
We show that, in contrast to the case of Laplace eigenfunctions, the nodal set of high energy eigenfunctions of the clamped plate problem is not necessarily dense, and can in fact…
Spectral geometry of the curl operator on smoothly bounded domains
Josef Greilhuber, Willi Kepplinger
We show that the spectrum of the curl operator on a generic smoothly bounded domain in three-dimensional Euclidean space consists of simple eigenvalues. The main new ingredient in…
More unit distances in arbitrary norms
Josef Greilhuber, Carl Schildkraut, Jonathan Tidor
For and any norm on , we prove that there exists a set of points that spans at least unit distances under this norm for every…
Quadratic cones on which few harmonic functions vanish
Josef Eberhard Greilhuber
We show that, in dimension three and higher, the space of harmonic functions vanishing on the cone defined by a generically chosen harmonic quadratic polynomial is two-dimensional.…
On Arnold's Transversality Conjecture for the Laplace--Beltrami Operator
Josef Greilhuber, Willi Kepplinger
This paper is concerned with the structure of the set of Riemannian metrics on a connected manifold such that the corresponding Laplace--Beltrami operator has an eigenvalue of a gi…
Regularity of CR maps into uniformly pseudoconvex hypersurfaces and applications to proper holomorphic maps
Josef Greilhuber, Bernhard Lamel
We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be u…