# Bubbling of quasiregular maps

## TL;DR

This paper extends Gromov's compactness theorem to quasiregular maps between closed manifolds, showing that sequences of such maps have convergent subsequences to a quasiregular map on a nodal manifold.

## Contribution

It provides a compactness result for quasiregular mappings, generalizing pseudoholomorphic curve theory to a broader class of maps between manifolds.

## Key findings

- Sequences of K-quasiregular maps with fixed degree have convergent subsequences.
- Convergence occurs to a quasiregular map on a nodal manifold.
- The result applies to maps between closed Riemannian manifolds.

## Abstract

We give a version of Gromov's compactess 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 $(f_n \colon M \to N)$ of $K$-quasiregular mappings of degree $D$ between closed Riemannian $d$-manifolds has a subsequence which converges to a $K$-quasiregular mapping $f\colon X\to N$ of degree $D$ on a nodal $d$-manifold $X$.