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math.DG2026
Deformation rigidity for Z/2 eigensections
Andriy Haydys, Siqi He, Willem Adriaan Salm
We prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More pre…
math.DG2026
Metric perturbations and deformations of k-nondegenerate Z/2-harmonic 1-forms
Siqi He, Willem Adriaan Salm
We study metric perturbations and deformation theory for degenerate Z/2-harmonic 1-forms. For a natural class of degenerate examples, we prove that after a suitable perturbation of…
math.DG2025
Search for Z/2 eigenfunctions on the sphere using machine learning
Andriy Haydys, Willem Adriaan Salm
We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we impleme…