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arXiv · 2510.11206

Hadamard-L\'{e}vy theorems for maps taking values in a finite dimensional space

Yacine Chitour·Zhengping Ji·Emmanuel Trélat
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Abstract

We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ 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.

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Yacine Chitour, Zhengping Ji, Emmanuel Trélat. 2025-10-13. Hadamard-L\'{e}vy theorems for maps taking values in a finite dimensional space. https://arxiv.org/abs/2510.11206

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