High dimensionality and h-principle in PDE

TL;DR

This paper discusses the Nash-Kuiper theorem from an analyst's perspective, emphasizing its connection to turbulence as an example of high-dimensional phenomena in PDEs.

Contribution

It offers a new analytical viewpoint on the Nash-Kuiper theorem and explores its relation to turbulence and high-dimensional PDE phenomena.

Findings

Highlights the connection between Nash-Kuiper theorem and turbulence

Provides an analysts' perspective on high-dimensional PDE phenomena

Suggests new insights into the role of high dimensions in PDEs

Abstract

In this note we would like to present "an analysts' point of view" on the Nash-Kuiper theorem and in particular highlight the very close connection to some aspects of turbulence -- a paradigm example of a high-dimensional phenomenon.