On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems.

@inproceedings{Cao2019OnNA,
  title={On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems.},
  author={Xinlin Cao and Huaian Diao and Hongyu Liu and Jun Zou},
  year={2019}
}
In this paper, we present some novel and intriguing findings on the geometric structures of Laplacian eigenfunctions and their deep relationship to the quantitative behaviours of the eigenfunctions in two dimensions. We introduce a new notion of generalized singular lines of the Laplacian eigenfunctions, and carefully study these singular lines and the nodal lines. The studies reveal that the intersecting angle between two of those lines is closely related to the vanishing order of the… CONTINUE READING
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