Jordan Domain Math

For a jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat 0 space and gromov hyperbolic.

Jordan domain math. Arxiv math 0512622v3 math dg 23 jul 2007 the intrinsic geometry of a jordan domain richard l. With respect to the cone topology that space plus its boundary at infinity is topologically the same as the original jordan domain. For a jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat 0 space and gromov hyperbolic.

With respect to the cone topol. It is not known if every jordan curve contains all four polygon vertices of some square but it has been proven true for sufficiently smooth curves and closed convex curves schnirelman 1944. Let sl denote a jordan domain in the extended complex plane the riemann sphere whose boundary includes a rectifiable arc a.

The term jordan domain cropped up in a paper i was reading and just couldn t find a definition on the internet. For a jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat 0 space and gromov hyperbolic. With respect to the cone topology that space plus its boundary at infinity is topologically the same as the original jordan domain.