| Abstract: |
| I will focus on a couple of properties of the eigenfunctions of
Steklov problem on a compact Riemannian manifold with boundary.
First, we give a precise
count of the interior critical points of a Steklov eigenfunction in terms of the
Euler characteristic of the manifold and of the number of its sign changes the boundary.
Based on a joint work with Luca Battaglia (University of Roma Tre)
and Luigi Provenzano (Sapienza University of Roma)
Next, we disprove the conjectured validity of Courant`s
theorem for the traces of Steklov eigenfunctions
building a Riemannian metric for which the n-th
eigenfunction has an arbitrary number of nodal domains on the boundary.
Based on a joint work with
Alberto Enciso (ICMAT Madrid) and Luigi Provenzano (Sapienza University of Roma) . |
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