5 citations · 7 across the 5 of their papers we have counts for
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Towards Constructing Geodesic Nets with Four Boundary Vertices and an Increasing Number of Balanced Vertices
Fabian Parsch, Hanrui Zhang
We construct a geodesic net in the plane with four boundary (unbalanced) vertices that has 25 balanced vertices and that is irreducible, i.e. it does not contain nontrivial subnets…
Geodesic Nets: Some Examples and Open Problems
Alexander Nabutovsky, Fabian Parsch
Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general propertie…
An example for a nontrivial irreducible geodesic net in the plane
Fabian Parsch
We construct a geodesic net in the plane with four unbalanced (boundary) vertices that has 16 balanced vertices and does not contain proper geodesic subnets. This is the first exam…
Geodesic nets with three boundary vertices
Fabian Parsch
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 t…