Equators Have at Most Countable Many Singularities with Bounded Total Angle

Authors

Pilar Herreros, University of PennsylvaniaFollow
Mario Ponce, Pontificia Universidad Catolica de ChileFollow
J.J.P. Veerman, Portland State UniversityFollow

Published In

Annales Academiae Scientiarum Fennicae. Mathematica

Document Type

Article

Publication Date

2017

Subjects

Boundary value problems

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. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …

Description

© 2017 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Locate the Document

https://doi.org/10.5186/aasfm.2017.4251

DOI

10.5186/aasfm.2017.4251

Persistent Identifier

https://archives.pdx.edu/ds/psu/30117

Citation Details

Herreros, P., Ponce, M., & Veerman, J. J. P. (2017, January). EQUATORS HAVE AT MOST COUNTABLE MANY SINGULARITIES WITH BOUNDED TOTAL ANGLE. In Annales Academiae Scientiarum Fennicae. Mathematica (Vol. 42, No. 2).