Proves upper semicontinuity of nodal domain counts under perturbations of Schrödinger operators on closed surfaces and constructs Courant-sharp metrics with prescribed boundary intersections.
Uhlenbeck, Generic properties of eigenfunctions, Amer
2 Pith papers cite this work. Polarity classification is still indexing.
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The authors establish new bounds on the Urschel number for graph Laplacian eigenvectors, including controls for multiple eigenvalues and classifications of zero vertices as shallow or deep.
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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.
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Urschel Nodal Domains via Perturbation Theory
The authors establish new bounds on the Urschel number for graph Laplacian eigenvectors, including controls for multiple eigenvalues and classifications of zero vertices as shallow or deep.