Some extensions of the class of $k$-convex bodies

V. Golubyatnikov V. Rovenski

Some extensions of the class of $k$-convex bodies

Metric Geometry 2015-12-31 v1 Differential Geometry

Authors: V. Golubyatnikov V. Rovenski

Abstract

We study relations of some classes of $k$ -convex, $k$ -visible bodies in Euclidean spaces. We introduce and study \textrm{circular projections} in normed linear spaces and classes of bodies related with families of such maps, in particular, \textrm{ $k$ -circular convex} and \textrm{ $k$ -circular visible} ones. Investigation of these bodies more general than $k$ -convex and $k$ -visible ones allows us to generalize some classical results of geometric tomography and find their new applications.

Keywords

k-convex bodies k-visible bodies circular projections normed linear spaces k-circular convex bodies k-circular visible bodies geometric tomography

Cite

@article{arxiv.0809.3643,
  title  = {Some extensions of the class of $k$-convex bodies},
  author = {V. Golubyatnikov V. Rovenski},
  journal= {arXiv preprint arXiv:0809.3643},
  year   = {2015}
}

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13 pages, 2 figures

Some extensions of the class of $k$-convex bodies

Abstract

Keywords

Cite

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