Abstract:
We give an overview of some new and old results on geometric properties
of eigenfunctions of Laplacians on Riemannian manifolds. We discuss
properties of nodal sets and critical points, the number of nodal domains,
and asymptotic properties of eigenfunctions in the high-energy
limit (such as weak * limits, the rate of growth of $L^p$ norms, and
relationships between positive and negative parts of eigenfunctions).
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