Indecomposable Quasiconformal Maps of Manifolds

TL;DR

This paper proves the existence of certain quasiconformal maps on closed manifolds that defy decomposition into simpler maps with minimal distortion.

Contribution

It introduces a new class of indecomposable quasiconformal maps on manifolds, challenging previous assumptions about their structure.

Findings

Existence of indecomposable quasiconformal maps on closed manifolds

Such maps cannot be expressed as compositions of maps with arbitrarily small conformal distortion

Provides a new perspective on the complexity of quasiconformal mappings

Abstract

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.