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math.AP2025
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…
math.AP2024
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.…