Bi-Lipschitzity of quasiconformal harmonic mappings in n-dimensional space with respect to k-metric

Abstract

We explore conditions which guarantee bi-Lipschitzity of harmonic quasiconformal maps with respect to k-metric. We prove that harmonic k-quasiconformal maps with nonzero Jacobian between any two domains in Rn are bi-Lipschitz with respect to k-metric, and prove the converse too.