C\'ordoba's differentation theorem: revisited

TL;DR

This paper revisits Cf3rdoba's differentiation theorem, providing a new proof of a three-dimensional case of Zygmund's conjecture using an exponential covering lemma that simplifies previous arguments.

Contribution

It introduces a novel proof technique for the three-dimensional case of Zygmund's conjecture, avoiding complex power series arguments.

Findings

Proves the three-dimensional case of Zygmund's conjecture

Introduces an exponential covering lemma

Simplifies previous proof methods

Abstract

In this paper we prove an exponential covering lemma implying the three dimensional case of a well-known conjecture formulated by A. Zygmund circa 1935 and solved by A. C\'ordoba in 1978. Our approach avoids a subtle argument involving the power series of the exponential function.