On the four vertex theorem in planes with radial density $e^{\phi \left(r\right)}$

Doan The Hieu, and Tran Le Nam. "On the four vertex theorem in planes with radial density $e^{φ(r)}$." Colloquium Mathematicae 113.1 (2008): 169-174. <http://eudml.org/doc/283436>.

@article{DoanTheHieu2008,
abstract = {It is shown that in a plane with a radial density the four vertex theorem holds for the class of all simple closed curves if and only if the density is constant. On the other hand, for the class of simple closed curves that are invariant under a rotation about the origin, the four vertex theorem holds for every radial density.},
author = {Doan The Hieu, Tran Le Nam},
journal = {Colloquium Mathematicae},
keywords = {Euclidean plane; radial density; simple closed curve; four vertex theorem; circle; curvature with density; plane with radial density},
language = {eng},
number = {1},
pages = {169-174},
title = {On the four vertex theorem in planes with radial density $e^\{φ(r)\}$},
url = {http://eudml.org/doc/283436},
volume = {113},
year = {2008},
}

TY - JOUR
AU - Doan The Hieu
AU - Tran Le Nam
TI - On the four vertex theorem in planes with radial density $e^{φ(r)}$
JO - Colloquium Mathematicae
PY - 2008
VL - 113
IS - 1
SP - 169
EP - 174
AB - It is shown that in a plane with a radial density the four vertex theorem holds for the class of all simple closed curves if and only if the density is constant. On the other hand, for the class of simple closed curves that are invariant under a rotation about the origin, the four vertex theorem holds for every radial density.
LA - eng
KW - Euclidean plane; radial density; simple closed curve; four vertex theorem; circle; curvature with density; plane with radial density
UR - http://eudml.org/doc/283436
ER -