2019/12/17 by Donaldson, Simon · 3 citations
#53C99 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1912.08274
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.