On the Four Vertex Theorem on planes with radial density $e^{φ(r)}$

Details On the Four Vertex Theorem on planes with radial density $e^{φ(r)}$ On the Four Vertex Theorem on planes with radial density $e^{φ(r)}$

2007-09-12

arxiv.org/abs/0709.1757v2

Mathematics

Differential Geometry

7 pages, 2figures

Scientific paper

It is showed that on 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. But 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.

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