2013/05/21 by Wei Wang, Wang, Wei · 2 citations
Mathematics · #34C25 #37J45 #58E05 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:34C25 #msc:37J45 #msc:58E05
paper · pdf · doi:10.48550/arxiv.1305.4680
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
arxiv created 2013/12/30 · arxiv updated 2013/12/31
In this paper, we prove there exist at least four geometrically distinct closed characteristics on every compact convex hypersurface \Sg in \R8. This gives a confirmed answer in the case n=4 to a long standing conjecture in Hamiltonian analysis since the time of A. M. Liapounov in 1892 (cf. P. 235 of \citeEke3).