  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 $R^{2n}$ conjectured by Ekeland.
