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math.SP2021
A counterexample to Payne's nodal line conjecture with few holes
Joel Dahne, Javier Gómez-Serrano, Kimberly Hou
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoff…
math.SP2017
Spectral determination of semi-regular polygons
Alberto Enciso, Javier Gómez-Serrano
Let us say that an -sided polygon is semi-regular if it is circumscriptible and its angles are all equal but possibly one, which is then larger than the rest. Regular polygons,…