Remarks on Radial Centres of Convex Bodies |
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| Authors: | Email author" target="_blank">I?HerburtEmail author M?Moszyńska Zbigniew?Peradzyński |
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| Institution: | (1) Department of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-601 Warszawa, Poland;(2) Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland;(3) Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland |
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| Abstract: | The paper concerns a family of selectors for convex bodies in Rn, radial centre maps, defined in the article of M. Moszyńska, Looking for selectors of star bodies, Geom. Dedicata 81 (2000), 131–147. A radial centre of a convex body A is the maximizer of a suitable generalized dual volume of A. We give physical interpretations of the notion of radial centre and study its geometric properties. We prove that these selectors are continuous with respect to the Hausdorff metric and solve the problem of direct additivity for radial centre of order α, which corresponds to the dual volume of order α.
Mathematics Subject Classifications (2005) 52A20, 52A40, 51P05, 85A25, 86A20. |
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| Keywords: | convex body continuous selector directly additive selector generalized dual volume gravitational centre radial centre |
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