On the four vertex theorem in planes with radial density $e^{\varphi(r)}$
Volume 113 / 2008
Colloquium Mathematicum 113 (2008), 169-174
MSC: Primary 53C25; Secondary 53A04.
DOI: 10.4064/cm113-1-10
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.
