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arXiv · 1602.03259

Cyclic Pursuit on Compact Manifolds

Dmitri Gekhtman
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Abstract

We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses in finite time or converges to a closed geodesic. The main result is that this conjecture is valid for nonpositively curved compact manifolds.

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Dmitri Gekhtman. 2016-02-10. Cyclic Pursuit on Compact Manifolds. https://doi.org/10.2140/pjm.2017.289.153

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