Zonoids with an equatorial characterization

Rafik Aramyan

Applications of Mathematics (2016)

  • Volume: 61, Issue: 4, page 413-422
  • ISSN: 0862-7940

Abstract

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It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid belongs to the class.

How to cite

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Aramyan, Rafik. "Zonoids with an equatorial characterization." Applications of Mathematics 61.4 (2016): 413-422. <http://eudml.org/doc/283406>.

@article{Aramyan2016,
abstract = {It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid belongs to the class.},
author = {Aramyan, Rafik},
journal = {Applications of Mathematics},
keywords = {integral geometry; convex body; zonoid; support function; integral geometry; convex body; zonoid; support function},
language = {eng},
number = {4},
pages = {413-422},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Zonoids with an equatorial characterization},
url = {http://eudml.org/doc/283406},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Aramyan, Rafik
TI - Zonoids with an equatorial characterization
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 413
EP - 422
AB - It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid belongs to the class.
LA - eng
KW - integral geometry; convex body; zonoid; support function; integral geometry; convex body; zonoid; support function
UR - http://eudml.org/doc/283406
ER -

References

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  6. Panina, G. Yu., Representation of an n -dimensional body in the form of a sum of ( n - 1 ) -dimensional bodies, Izv. Akad. Nauk Arm. SSR, Mat. 23 (1988), 385-395 Russian translation in Sov. J. Contemp. Math. Anal. 23 (1988), 91-103. (1988) Zbl0679.52006MR0997401
  7. Schneider, R., 10.1002/mana.19700440105, Math. Nachr. 44 (1970), 55-75 German. (1970) Zbl0162.54302MR0275286DOI10.1002/mana.19700440105
  8. Schneider, R., Convex Bodies: the Brunn-Minkowski Theory, Encyclopedia of Mathematics and Its Applications 44 Cambridge University Press, Cambridge (1993). (1993) Zbl0798.52001MR1216521
  9. Schneider, R., Weil, W., Zonoids and Related Topics, Convexity and Its Applications Birkhäuser, Basel (1983), 296-317. (1983) Zbl0524.52002MR0731116
  10. Weil, W., 10.1007/BF01220469, Arch. Math. 29 (1977), 655-659 German. (1977) Zbl0382.52006MR0513967DOI10.1007/BF01220469

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