Decomposing diffeomorphisms of the sphere

TL;DR

This paper demonstrates that any sphere diffeomorphism can be broken down into small, controlled bi-Lipschitz maps with minimal distortion and point movement, enhancing understanding of sphere transformations.

Contribution

It introduces a novel decomposition method for sphere diffeomorphisms into low-distortion, small-movement bi-Lipschitz components.

Findings

Any sphere diffeomorphism can be decomposed into bi-Lipschitz maps with small isometric distortion.

The decomposition ensures minimal point displacement in the spherical metric.

This advances the understanding of the structure of sphere diffeomorphisms.

Abstract

We prove that any diffeomorphism of the sphere S^n to itself can be decomposed into bi-Lipschitz mappings of small isometric distortion and which move points a small amount in the spherical metric.