Regularity of Mediatrices in SurfacesMathematics and Statistics Faculty Publications and Presentations
- Boundary Conditions (Differential Equations),
- Differential geometry
AbstractFor distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. This paper establishes additional geometric regularity properties of mediatrices. We show that mediatrices have the radial linearizability property, which implies that at each point they have a geometrically defined derivative in the branching directions. Also, we study the particular case of mediatrices on spheres, by showing that they are Lipschitz simple closed curves exhibiting at most countably many singularities, with finite total angular deficiency.
Citation InformationPilar Herreros, Mario Ponce and J. J. P. Veerman. "Regularity of Mediatrices in Surfaces" (2014)
Available at: http://works.bepress.com/jj-veerman/6/