A short proof that the $L^p$-diameter of $Diff_0(S,area)$ is infinite

TL;DR

This paper provides a concise proof demonstrating that the $L^p$-diameter of the group of area-preserving diffeomorphisms isotopic to the identity on a compact surface is infinite, highlighting a fundamental geometric property.

Contribution

It offers a new, simplified proof establishing the infinite $L^p$-diameter for a key class of diffeomorphism groups on surfaces.

Findings

The $L^p$-diameter of the group is infinite.

The proof is notably shorter than previous approaches.

The result applies to all compact surfaces with area-preserving diffeomorphisms.

Abstract

We give a short proof that the $L^p$-diameter of the group of area preserving diffeomorphisms isotopic to the identity of a compact surface is infinite.