Orthogonal Projection of Convex Sets with a Differentiable Boundary

Autor:	Bainier, Gustave, Marx, Benoit, Ponsart, Jean-Christophe
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematics - General Topology 52A20 53A07
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.08937 Zobrazit plný text záznamu View this record from Arxiv