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arXiv · 1807.00887

Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles

Roberto Giambò·Fabio Giannoni·Paolo Piccione
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Abstract

We use nonsmooth critical point theory and the theory of geodesics with obstacle to show a multiplicity result about orthogonal geodesic chords in a Riemannian manifold (with boundary) which is homeomorphic to an $N$-disk. This applies to brake orbits in a potential well of a natural Hamiltonian system, providing a further step towards the proof of a celebrated conjecture by Seifert.

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Roberto Giambò, Fabio Giannoni, Paolo Piccione. 2018-07-02. Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles. https://arxiv.org/abs/1807.00887

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