Deformation rigidity for Z/2 eigensections
Differential Geometry
2026-04-21 v1
Abstract
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 precisely, we show that every minimal non-degenerate critical eigensection is deformation rigid: any sufficiently small deformation of the configuration that still admits a critical eigensection must come from an SO(3)-rotation. This generalizes the rigidity phenomenon previously discovered in symmetric examples of Taubes-Wu.
Cite
@article{arxiv.2604.17044,
title = {Deformation rigidity for Z/2 eigensections},
author = {Andriy Haydys and Siqi He and Willem Adriaan Salm},
journal= {arXiv preprint arXiv:2604.17044},
year = {2026}
}
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9 Pages