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Equators Have at Most Countable Many Singularities with Bounded Total Angle
Annales Academiae Scientiarum Fennicae. Mathematica
  • Pilar Herreros, University of Pennsylvania
  • Mario Ponce, Pontificia Universidad Catolica de Chile
  • J.J.P. Veerman, Portland State University
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  • Boundary value problems

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 …


© 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 (

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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).