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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.08937 |
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| _version_ | 1866916326632587264 |
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| author | Bainier, Gustave Marx, Benoit Ponsart, Jean-Christophe |
| author_facet | Bainier, Gustave Marx, Benoit Ponsart, Jean-Christophe |
| contents | Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior) and the boundary of its orthogonal projection onto the linear subspaces of the Euclidean space. A system of equations for these orthogonal projections is derived from this topological link. This result is illustrated by the projection of the unit ball of norm $4$ in $\mathbb{R}^3$ on a plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08937 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orthogonal Projection of Convex Sets with a Differentiable Boundary Bainier, Gustave Marx, Benoit Ponsart, Jean-Christophe Differential Geometry General Topology 52A20, 53A07 Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior) and the boundary of its orthogonal projection onto the linear subspaces of the Euclidean space. A system of equations for these orthogonal projections is derived from this topological link. This result is illustrated by the projection of the unit ball of norm $4$ in $\mathbb{R}^3$ on a plane. |
| title | Orthogonal Projection of Convex Sets with a Differentiable Boundary |
| topic | Differential Geometry General Topology 52A20, 53A07 |
| url | https://arxiv.org/abs/2302.08937 |