{"ID":2856239,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11206","arxiv_id":"2510.11206","title":"Hadamard-Lévy theorems for maps taking values in a finite dimensional space","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.11206","url_pdf":"https://arxiv.org/pdf/2510.11206v1","authors":"[\"Yacine Chitour\",\"Zhengping Ji\",\"Emmanuel Trélat\"]","published":"2025-10-13T09:42:28Z","proceeding":"math.CA","tasks":"[\"math.CA\",\"math.OC\"]","methods":"[]","has_code":false}