Bubbling of quasiregular maps

Abstract

We give a version of Gromov’s compactness theorem for pseudoholomorphic curves in the case of quasiregular mappings between closed manifolds. More precisely we show that, given \(K\ge 1\) and \(D\ge 1\), any sequence \((f_n :M \rightarrow N)\) of K-quasiregular mappings of degree D between closed Riemannian d-manifolds has a subsequence which converges to a K-quasiregular mapping \(f:X\rightarrow N\) of degree D on a nodal d-manifold X.