Proves upper semicontinuity of nodal domain counts under perturbations of Schrödinger operators on closed surfaces and constructs Courant-sharp metrics with prescribed boundary intersections.
Nadirashvili, Metric properties of eigenfunctions of the L aplace operator on manifolds , Ann
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Nodal Domains on Surfaces under Perturbation: Upper Semicontinuity, Courant-Sharpness, and Boundary Intersections
Proves upper semicontinuity of nodal domain counts under perturbations of Schrödinger operators on closed surfaces and constructs Courant-sharp metrics with prescribed boundary intersections.