Higher order Goh conditions for singular extremals of corank 1

TL;DR

This paper establishes higher order Goh conditions for singular extremals of corank 1, expanding understanding of length minimizing curves under specific differential vanishing conditions.

Contribution

It introduces higher order Goh conditions for corank 1 singular extremals, based on an open mapping theorem for maps with non-singular differentials.

Findings

Proves Goh conditions of order n for certain singular curves

Relies on an open mapping theorem for non-singular nth differentials

Provides conditions under which length minimizing curves are characterized

Abstract

We prove Goh conditions of order n for strictly singular length minimizing curves of corank 1, under the assumption that the lower order intrinsic differentials of the end-point map vanish. This result relies upon the proof of an open mapping theorem for maps with non-singular nth differential.