Reconstruction of Three Dimensional Convex Bodies from the Curvatures of Their Shadows

• 作者: Rafik Aramyan
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: INTEGRAL Geometry CONVEX Body PROJECTION CURVATURE Support Function
• 年，卷（期）: 2015,（2）
• 页码范围: 86-95
• 页数: 10页
• 分类号: O1

摘要

In this article, we study necessary and sufficient conditions for a function, defined on the space of flags to be the projection curvature radius function for a convex body. This type of inverse problems has been studied by Christoffel, Minkwoski for the case of mean and Gauss curvatures. We suggest an algorithm of reconstruction of a convex body from its projection curvature radius function by finding a representation for the support function of the body. We lead the problem to a system of differential equations of second order on the sphere and solve it applying a consistency method suggested by the author of the article.