We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deformations of the data. The proof is an application of a version of the Nash-Moser implicit function theorem.

中文翻译：

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多值调和函数的变形

我们在黎曼流形中的余维 2 子流形的补集上考虑束的谐波部分，可以将其视为多值谐波函数。我们证明了一个结果，即这些在数据的小变形下是稳定的。证明是 Nash-Moser 隐函数定理的一个版本的应用。