Some extensions of the class of convex bodies

Details Some extensions of the class of convex bodies Some extensions of the class of convex bodies

2008-08-13

arxiv.org/abs/0808.1788v3

Mathematics

Differential Geometry

Scientific paper

We introduce and study a new class of $\eps$-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how $\eps$-convex bodies connect with some classical results of Convex Geometry, as Helly theorem, and find applications to geometric tomography. We introduce the notion of a circular projection and investigate the problem of determination of $\eps$-convex bodies by their projection-type images. The results generalize corresponding stability theorems by H. Groemer.

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