English

Closed characteristics on compact convex hypersurfaces in $\R^8$

Symplectic Geometry 2013-12-31 v3 Differential Geometry

Abstract

In this paper, we prove there exist at least four geometrically distinct closed characteristics on every compact convex hypersurface \Sg\Sg in R8\R^8. This gives a confirmed answer in the case n=4n=4 to a long standing conjecture in Hamiltonian analysis since the time of A. M. Liapounov in 1892 (cf. P. 235 of \cite{Eke3}).

Keywords

Cite

@article{arxiv.1305.4680,
  title  = {Closed characteristics on compact convex hypersurfaces in $\R^8$},
  author = {Wei Wang},
  journal= {arXiv preprint arXiv:1305.4680},
  year   = {2013}
}

Comments

62 pages. Some details are added and some typos are corrected in this version. arXiv admin note: substantial text overlap with arXiv:1112.5501, arXiv:math/0701673, arXiv:math/0701608

R2 v1 2026-06-22T00:19:30.286Z