The theory of graph-like Legendrian unfoldings and its applications

TL;DR

This survey reviews recent advances in the theory of graph-like Legendrian unfoldings, highlighting their applications in wave front propagation and including some new results and corrected proofs.

Contribution

It provides a comprehensive overview of graph-like Legendrian unfoldings and introduces new original results along with corrected proofs.

Findings

Introduction of new results in Legendrian unfoldings

Corrected proofs of existing theorems

Applications to wave front propagation

Abstract

This is mainly a survey article on the recent development of the theory of graph-like Legendrian unfoldings and its applications. The notion of big Legendrian submanifolds was introduced by Zakalyukin for describing the wave front propagations. Graph-like Legendrian unfoldings belong to a special class of big Legendrian submanifolds. Although this is a survey article, some new original results and the corrected proofs of some results are given.