4 papers
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…
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…
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…
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…