Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 67-77
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R. N. Karasev. On transversals of the family of translates of two-dimensional convex compact. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 67-77. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a7/
@article{ZNSL_1998_252_a7,
author = {R. N. Karasev},
title = {On transversals of the family of translates of two-dimensional convex compact},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {67--77},
year = {1998},
volume = {252},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a7/}
}
TY - JOUR
AU - R. N. Karasev
TI - On transversals of the family of translates of two-dimensional convex compact
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1998
SP - 67
EP - 77
VL - 252
UR - http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a7/
LA - ru
ID - ZNSL_1998_252_a7
ER -
%0 Journal Article
%A R. N. Karasev
%T On transversals of the family of translates of two-dimensional convex compact
%J Zapiski Nauchnykh Seminarov POMI
%D 1998
%P 67-77
%V 252
%U http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a7/
%G ru
%F ZNSL_1998_252_a7
The following theorem gives an affirmative answer to Grünbaum's old equistion. Let $\mathscr K$ be the family of translates of a convex compact set $K\subset\mathbb R^2$. If every two elements of $\mathscr K$ have a common point, then there exist three points $A,B,C\in\mathbb R^2$ such that every element of $\mathscr K$ contains some of these points.
