Geodesic
On the four vertex theorem in planes with radial density $e^{\varphi(r)}$
Doan The Hieu 1   ; Tran Le Nam 1
1 College of Education, Hue University 34 Le Loi, Hue, Vietnam
Colloquium Mathematicum, Tome 113 (2008) no. 1, pp. 169-174 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm113-1-10
Keywords: shown plane radial density vertex theorem holds class simple closed curves only density constant other class simple closed curves invariant under rotation about origin vertex theorem holds every radial density

Doan The Hieu  1   ; Tran Le Nam  1

1 College of Education, Hue University 34 Le Loi, Hue, Vietnam 
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Doan The Hieu; Tran Le Nam. On the four vertex theorem in planes with
 radial density $e^{\varphi(r)}$. Colloquium Mathematicum, Tome 113 (2008) no. 1, pp. 169-174. doi: 10.4064/cm113-1-10

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