Quasiregular curves: Hölder continuity and higher integrability

Abstract

We show that a $K$-quasiregular $\omega$-curve from a Euclidean domain to a Euclidean space with respect to a covector $\omega$ is locally $(1/K)(\Vert \omega \Vert /|\omega {|}_{{\ell }_1})$-Hölder continuous. We also show that quasiregular curves enjoy higher integrability.