Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in R-2n
Multiplicity and ellipticity of closed characteristics on compact star-shaped hypersurfaces in R-2n
复制标题
R-2n中致密星形超曲面闭合特性的多重性和椭圆性
DOI：
10.1007/s00526-017-1173-1
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发表时间：
2017
影响因子：
2.1
通讯作者：
Hui Liu
中科院分区：
文献类型：
--
作者：
Huagui Duan;Hui Liu
本文首先将Ekeland和霍费尔（Commun Math Phys 113：419-467，1987）关于紧致凸超曲面的闭特征的一些理论推广到星形超曲面。作为应用，我们利用Ekeland-Hellman理论和指数迭代理论证明了：如果一个不满足适当pinching条件的紧致星形超曲面恰好具有两个几何上不同的闭特征，则它们都是椭圆的.我们还得出Long和Zhu（Ann Math 155：317-368，2002）的理论对于动力凸星形超曲面仍然成立，并将其与Wang等人（杜克数学J 139：411-462，2007），Liu等人（J Funct Anal 266：5598-5638，2014）和Wang（Adv Math 297：93-148，2016）的结果相结合，我们得到了在动力凸星形超曲面上至少存在一个不闭特征.
In this paper, we firstly generalize some theories developed by Ekeland and Hofer (Commun Math Phys 113:419–467, 1987) for closed characteristics on compact convex hypersurfaces into star-shaped hypersurfaces. As applications we use Ekeland–Hofer theory and index iteration theory to prove that if a compact star-shaped hypersuface insatisfying some suitable pinching condition carries exactly two geometrically distinct closed characteristics, then both of them must be elliptic. We also conclude that the theory developed by Long and Zhu (Ann Math 155:317–368, 2002) still holds for dynamically convex star-shaped hypersurfaces, and combining it with the results in Wang et al. (Duke Math J 139:411–462, 2007), Liu et al. (J Funct Anal 266:5598–5638, 2014) and Wang (Adv Math 297:93–148, 2016), we obtain that there exist at leastnclosed characteristics on every dynamically convex star-shaped hypersurface infor.