A note on the concurrent normal conjecture

It is conjectured since long that for any convex body K ∈ R n there exists a point in the interior of K which belongs to at least 2 n normals from different points on the boundary of K . The conjecture is known to be true for n = 2, 3, 4. Motivated by a recent preprint of Y. Martinez-Maure [4], we g...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2022, Vol.167 (2), p.529-532
Main Authors: Grebennikov, A., Panina, G.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:It is conjectured since long that for any convex body K ∈ R n there exists a point in the interior of K which belongs to at least 2 n normals from different points on the boundary of K . The conjecture is known to be true for n = 2, 3, 4. Motivated by a recent preprint of Y. Martinez-Maure [4], we give a short proof of his result: for dimension n ≥ 3 , under mild conditions, almost every normal through a boundary point to a smooth convex body K ∈ R n contains an intersection point of at least 6 normals from different points on the boundary of K .
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-022-01251-0