| Title:
|
Zonoids with an equatorial characterization (English) |
| Author:
|
Aramyan, Rafik |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
413-422 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
integral geometry |
| Keyword:
|
convex body |
| Keyword:
|
zonoid |
| Keyword:
|
support function |
| MSC:
|
52A15 |
| MSC:
|
53C45 |
| MSC:
|
53C65 |
| idZBL:
|
Zbl 06644004 |
| idMR:
|
MR3532251 |
| DOI:
|
10.1007/s10492-016-0139-5 |
| . |
| Date available:
|
2016-08-01T09:24:15Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145793 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[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. Zbl 0679.52006, MR 0997401 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
