2009/01/18 by Renyi Ma, Ma, Renyi
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM
paper · pdf · doi:10.48550/arxiv.0901.2440
arXiv admin note: substantial text overlap with arXiv:math/0603282; text overlap with arXiv:0705.2884 by other authors
arxiv created 2013/06/17 · arxiv updated 2013/09/26
In this article, we first give a proof on the Arnold chord conjecture which states that every Reeb flow has at least as many Reeb chords as a smooth function on the Legendre submanifold has critical points on contact manifold. Second, we prove that every Reeb flow has at least as many close Reeb orbits as a smooth round function on the close contact manifold has critical circles on contact manifold. This also implies a proof on the fact that there exists at least number n close Reeb orbits on close (2n-1)-dimensional convex hypersurface in R2n conjectured by Ekeland.