On Projection Bodies of Order One
[摘要] The projection body of order one $Pi_1K$ of a convex body $K$ in$R^n$ is the body whose support function is, up to a constant, theaverage mean width of the orthogonal projections of $K$ ontohyperplanes through the origin.The paper contains an inequality for the support function of$Pi_1K$, which implies in particular that such a function isstrictly convex, unless $K$ has dimension one or two. Furthermore,an existence problem related to the reconstruction of a convex bodyis discussed to highlight the different behavior of the areameasures of order one and of order $n-1$.
[发布日期] [发布机构]
[效力级别] [学科分类] 数学（综合）
[关键词] almost smooth convex body;convex body of constant width;weakly neighbourly antipodal convex polytope;Illumination Conjecture;X-ray number;X-ray Conjecture [时效性]
