TY - JOUR

T1 - A note on the concurrent normal conjecture

AU - Grebennikov, A.

AU - Panina, G.

N1 - Publisher Copyright: © 2022, Akadémiai Kiadó, Budapest, Hungary.

PY - 2022/8

Y1 - 2022/8

N2 - It is conjectured since long that for anyconvex body K∈ Rn there exists a point inthe interior of K which belongs to at least 2n normals from different points on theboundary 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 normalthrough a boundary point to a smooth convex body K∈ Rn contains an intersection point of at least 6 normals from different points on the boundary of K.

AB - It is conjectured since long that for anyconvex body K∈ Rn there exists a point inthe interior of K which belongs to at least 2n normals from different points on theboundary 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 normalthrough a boundary point to a smooth convex body K∈ Rn contains an intersection point of at least 6 normals from different points on the boundary of K.

KW - bifurcation

KW - Morse point

KW - Morse–Cerf theory

UR - http://www.scopus.com/inward/record.url?scp=85134704857&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f4ce48a0-80c6-353f-9fa9-4a4690780d61/

U2 - 10.1007/s10474-022-01251-0

DO - 10.1007/s10474-022-01251-0

M3 - Article

AN - SCOPUS:85134704857

VL - 167

SP - 529

EP - 532

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 2

ER -