Plane rectifiable curves: old and new

TL;DR

This paper revisits classical concepts of algebraically rectifiable plane curves, introduces new criteria, relates them to quadratic differentials, and extends the notion to higher-order differentials.

Contribution

It provides novel criteria for algebraic rectifiability, connects it with quadratic differentials, and generalizes the concept to higher-order differentials.

Findings

New criteria for algebraic rectifiability introduced

Relation established between rectifiability and quadratic differentials

Generalization to differentials of higher order achieved

Abstract

In this note we recall the classical notion of an algebraically rectifiable plane curve going back to J. A. Serret, E. Laguerre and G. Humbert. We provide new criteria of algebraic rectifiability, relate this notion to quadratic differentials, and generalize it to differentials of higher order.