Nodal sets of thin curved layers

  title={Nodal sets of thin curved layers},
  author={David Krej{\vc}iř{\'i}k and Matěj Tu{\vs}ek},
Abstract This paper is concerned with the location of nodal sets of eigenfunctions of the Dirichlet Laplacian in thin tubular neighbourhoods of hypersurfaces of the Euclidean space of arbitrary dimension. In the limit when the radius of the neighbourhood tends to zero, it is known that spectral properties of the Laplacian are approximated well by an effective Schrodinger operator on the hypersurface with a potential expressed solely in terms of principal curvatures. By applying techniques of… CONTINUE READING
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