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Article
Regularity of Mediatrices in Surfaces
Mathematics and Statistics Faculty Publications and Presentations
  • Pilar Herreros
  • Mario Ponce
  • J. J. P. Veerman, Portland State University
Document Type
Pre-Print
Publication Date
1-1-2014
Subjects
  • Boundary Conditions (Differential Equations),
  • Differential geometry
Abstract

For 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.

Description

Pre-print of an article submitted for consideration to be published.

Persistent Identifier
http://archives.pdx.edu/ds/psu/17529
Citation Information
Pilar Herreros, Mario Ponce and J. J. P. Veerman. "Regularity of Mediatrices in Surfaces" (2014)
Available at: http://works.bepress.com/jj-veerman/6/