Papers › A counterexample to Payne's nodal line conjecture with few holes
A counterexample to Payne's nodal line conjecture with few holes
Joel Dahne, Javier Gómez-Serrano, Kimberly Hou
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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, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.
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