# Nodal Set Openings on Perturbed Rectangular Domains

@inproceedings{Beck2022NodalSO, title={Nodal Set Openings on Perturbed Rectangular Domains}, author={Thomas Beck and Marichi Gupta and Jeremy Louis Marzuola}, year={2022} }

. We study the eﬀects of perturbing the boundary of a rectangle on the nodal sets of eigenfunctions of the Laplacian. Namely, for a rectangle of a given aspect ratio N , we identify the ﬁrst Dirichlet mode to feature a crossing in its nodal set and perturb one of the sides of the rectangle by a close to ﬂat, smooth curve. Such perturbations will often “open” the crossing in the nodal set, splitting it into two curves, and we study the separation between these curves and their regularity. The…

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