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September 2021 Geodesic nets with three boundary vertices
Fabian Parsch
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J. Differential Geom. 119(1): 99-140 (September 2021). DOI: 10.4310/jdg/1631124286

Abstract

We prove that a geodesic net with three boundary (= unbalanced) vertices on a non-positively curved plane has at most one balanced vertex. We do not assume any a priori bound for the degrees of unbalanced vertices.

The result seems to be new even in the Euclidean case.

We demonstrate by examples that the result is not true for metrics of positive curvature on the plane, and that there are no immediate generalizations of this result for geodesic nets with four unbalanced vertices.

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Fabian Parsch. "Geodesic nets with three boundary vertices." J. Differential Geom. 119 (1) 99 - 140, September 2021. https://doi.org/10.4310/jdg/1631124286

Information

Received: 12 April 2018; Accepted: 11 March 2019; Published: September 2021
First available in Project Euclid: 10 September 2021

Digital Object Identifier: 10.4310/jdg/1631124286

Rights: Copyright © 2021 Lehigh University

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Vol.119 • No. 1 • September 2021
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