On quasiconformal maps with identity boundary values

TL;DR

This paper investigates quasiconformal homeomorphisms of the unit ball in higher dimensions that fix the boundary, establishing a spatial analogue of Teichmüller's theorem to deepen understanding of their properties.

Contribution

It proves a higher-dimensional analogue of Teichmüller's theorem for quasiconformal maps with identity boundary values.

Findings

Established a spatial analogue of Teichmüller's theorem.

Characterized quasiconformal maps fixing the boundary in higher dimensions.

Abstract

Quasiconformal homeomorphisms of the unit ball $B^n$ of ${\mathbb R}^n, n \ge 3,$ onto itself with identity boundary values are studied. A spatial analogue of Teichm\"uller's theorem is proved.