Hadamard-L\'{e}vy theorems for maps taking values in a finite dimensional space
Classical Analysis and ODEs
2025-10-14 v1 Optimization and Control
Abstract
We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a differentiable map from a Hilbert space to a finite-dimensional Euclidean space, when its second-order differential has uniform upper and lower bounds, it has a global path-lifting property in the presence of singularities. This is then applied to the nonlinear motion planning problem, establishing in some cases the well-posedness of the continuation method despite critical values of the endpoint maps.
Cite
@article{arxiv.2510.11206,
title = {Hadamard-L\'{e}vy theorems for maps taking values in a finite dimensional space},
author = {Yacine Chitour and Zhengping Ji and Emmanuel Trélat},
journal= {arXiv preprint arXiv:2510.11206},
year = {2025}
}