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Some extensions of the class of k-convex bodies

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Abstract

We study interrelations between some classes of bodies in Euclidean spaces. We introduce circular projections in normed linear spaces and the classes of bodies related with some families of these projections. Investigation of these bodies more general than k-convex and k-visible bodies allows us to generalize some classical results of geometric tomography and find their new applications.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    V. P. Golubyatnikov & V. Yu. Rovenski

Authors
  1. V. P. Golubyatnikov
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  2. V. Yu. Rovenski
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Correspondence to V. Yu. Rovenski.

Additional information

To Yuriĭ Grigor’evich Reshetnyak on his 80th birthday.

Original Russian Text Copyright © 2009 Golubyatnikov V. P. and Rovenski V. Yu.

The authors were partially supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-8526.2006.1), the Program “Development of the Scientific Potential of Higher School” of the Ministry for Education of the Russian Federation (Grant 2.1.1/3707), and Stipend FP7-PEOPLE-2007-2-1-IEF, No. 219696 of Marie-Curie action.

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Novosibirsk; Haifa. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 5, pp. 1037–1049, September–October, 2009.

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Golubyatnikov, V.P., Rovenski, V.Y. Some extensions of the class of k-convex bodies. Sib Math J 50, 820–829 (2009). https://doi.org/10.1007/s11202-009-0092-6

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  • DOI: https://doi.org/10.1007/s11202-009-0092-6

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