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Ellipsoid characterization theorems |
Tartalom: | http://www.degruyter.com/view/j/advg.2013.13.issue-1/advg... |
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Archívum: | MTA Könyvtár |
Gyűjtemény: |
Status = Published
Type = Article |
Cím: |
Ellipsoid characterization theorems
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Létrehozó: |
Lángi, Zsolt
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Dátum: |
2013-01-08
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Téma: |
QA73 Geometry / geometria
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Tartalmi leírás: |
In this note we prove two ellipsoid characterization theorems. The first one is that if K is a convex body in a normed space with unit ball M, and for any point p ? K and in any 2-dimensional plane P intersecting intK and containing p, there are two tangent segments of the same normed length from p to K, then K and M are homothetic ellipsoids. Furthermore, we show that if M is the unit ball of a strictly convex, smooth norm, and in this norm billiard angular bisectors coincide with Busemann angular bisectors or Glogovskij angular bisectors, then M is an ellipse.
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Típus: |
Article
PeerReviewed
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Formátum: |
text
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Azonosító: |
Lángi, Zsolt (2013) Ellipsoid characterization theorems. Advances in Geometry, 13 (1). pp. 145-154. ISSN 1615-7168
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Kapcsolat: |