Payne's nodal line conjecture fails on doubly-connected planar domains

Published 28 Oct 2025 in math.AP | (2510.24436v1)

Abstract: We present examples of bounded planar domains with one single hole for which the nodal line of a second Dirichlet eigenfunction is closed and does not touch the boundary. This shows that Payne's nodal line conjecture can at most hold for simply-connected domains in the plane.

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