Document Type

Pre-Print

Publication Date

2014

Subjects

Boundary value problems, Differential geometry, Riemannian manifolds

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

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