English

Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles

Dynamical Systems 2018-07-04 v1

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 NN-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.

Keywords

Cite

@article{arxiv.1807.00887,
  title  = {Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles},
  author = {Roberto Giambò and Fabio Giannoni and Paolo Piccione},
  journal= {arXiv preprint arXiv:1807.00887},
  year   = {2018}
}

Comments

24 pages. Accepted for publication on Calc Var PDE

R2 v1 2026-06-23T02:48:42.981Z