Abstract
We study the behavior of the successive inner and outer radii with respect to the Firey p-sums of convex bodies, where p ≥ 1. For all p ≥ 1 we get upper and lower bounds for the radii of the p-sum of two convex bodies in terms of the radii of the sets. These results generalize the corresponding relations for the classical Minkowski addition.
Keywords: Successive inner and outer radii; p-sum.
References
Published Online: 2014-01-17
Published in Print: 2014-01
© 2014 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Real hypersurfaces of complex and quaternionic hyperbolic spaces
- Toric geometry of the 3-Kimura model for any tree
- Invariant surfaces in Sol3 with constant mean curvature and their computer graphics
- A short geometric proof that Hausdorff limits are definable in any o-minimal structure
- Seshadri constants on smooth threefolds
- Visible shoreline results for staircase paths in ℝd
- Characterization of isometric embeddings of Grassmann graphs
- Typical simplicially convex bodies
- On successive radii of p-sums of convex bodies
- Resolving sets for four families of distance-regular graphs
- White-black graphs and right-angled hyperbolic handlebodies
- Scalar and Ricci curvatures of special contact slant submanifolds in Sasakian space forms
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- Collineation groups of topological parallelisms