3 papers
math.DG2026
On spectral simplicity of the Hodge Laplacian and Curl Operator along paths of metrics
Willi Kepplinger
We prove that the curl operator on closed oriented -manifolds, i.e., the square root of the Hodge Laplacian on its coexact spectrum, generically has -dimensional eigenspaces,…
math.DG2026
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…
math.SP2025
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…