Nodal sets of eigenfunctions, Antonie Stern’s results revisited
Séminaire de théorie spectrale et géométrie, Volume 32  (2014-2015), p. 1-37

These notes present a partial survey of our recent contributions to the understanding of nodal sets of eigenfunctions (constructions of families of eigenfunctions with few or many nodal domains, equality cases in Courant’s nodal domain theorem), revisiting Antonie Stern’s thesis, Göttingen, 1924.

DOI : https://doi.org/10.5802/tsg.302
Classification:  35P15,  49R50
Keywords: Nodal domains, Courant theorem, Pleijel theorem, Dirichlet Laplacian
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     author = {B\'erard, Pierre and Helffer, Bernard},
     title = {Nodal sets of eigenfunctions, Antonie Stern's results revisited},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     year = {2014-2015},
     pages = {1-37},
     doi = {10.5802/tsg.302},
     language = {en},
     url = {http://www.numdam.org/item/TSG_2014-2015__32__1_0}
}
Bérard, Pierre; Helffer, Bernard. Nodal sets of eigenfunctions, Antonie Stern’s results revisited. Séminaire de théorie spectrale et géométrie, Volume 32 (2014-2015) , pp. 1-37. doi : 10.5802/tsg.302. http://www.numdam.org/item/TSG_2014-2015__32__1_0/

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