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


Shadia Shalandi




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 $\mathbb{R}^n$ are bi-Lipschitz with respect to $k$-metric, and prove the converse too.