Wave front evolution and pedal evolution

TL;DR

This paper extends the calculus correspondence between pedal evolutions and wave front evolutions to multi-parameter cases and explores potential generalizations to degenerate cases, with applications.

Contribution

It introduces multi-parameter extensions of the calculus correspondence and discusses possible generalizations to degenerate evolutions.

Findings

Extended calculus correspondence to multi-parameter evolutions.

Provided applications of the extended calculus correspondence.

Discussed potential generalizations to degenerate evolutions.

Abstract

The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the possibility of generalization of the calculus correspondence to degenerate pedal evolutions and degenerate wave front evolutions.