Arnold弦猜想的一个证明
A Proof On Arnold Chord Conjecture
摘要：
本文首先证明了Arnold弦猜想，即Legendre子流形上的光滑函数在切触流形上的临界点至少等于每个Reeb流的Reeb弦数.其次，证明了闭切触流形上的光滑圆函数在切触流形上的临界圆个数至少等于闭Reeb流的闭Reeb轨道个数。这也证明了在Ekeland证明的$R^{2n}$中的闭$(2n-1)$维凸超曲面上至少存在多个$n$闭Reeb轨道.
英文摘要：
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.
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