Proves upper semicontinuity of nodal domain counts under perturbations of Schrödinger operators on closed surfaces and constructs Courant-sharp metrics with prescribed boundary intersections.
Michor, and Armin Rainer, Denjoy- C arleman differentiable perturbation of polynomials and unbounded operators , Integral Equations Operator Theory 71 (2011), no
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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.