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

Tom 113 / 2008

Doan The Hieu, Tran Le Nam Colloquium Mathematicum 113 (2008), 169-174 MSC: Primary 53C25; Secondary 53A04. DOI: 10.4064/cm113-1-10

Streszczenie

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.

Autorzy

  • Doan The HieuCollege of Education, Hue University
    34 Le Loi, Hue, Vietnam
    e-mail
    e-mail
  • Tran Le NamCollege of Education, Hue University
    34 Le Loi, Hue, Vietnam

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