Weil-Petersson Teichmüller space II: Smoothness of flow curves of H32 -vector fields
Weil-Petersson Teichmüller space II: Smoothness of flow curves of H32 -vector fields
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Weil-Petersson Teichmuller 空间 II：H-3/2 矢量场的流动曲线的平滑度
DOI：
10.1016/j.aim.2019.106891
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发表时间：
2019
影响因子：
1.7
通讯作者：
Tang Shuan
中科院分区：
文献类型：
--
作者：
Shen Yuliang;Tang Shuan
给定单位圆s1上Sobolev类h32的连续向量场λ (t,⋅)，微分方程{d η d t= λ (t, η) η (0, ζ)= ζ的流图η= g （t,⋅）为拟对称同胚。最近，guy - balmaz - ratiu[15]推测流动曲线g （t,⋅）属于Weil-Petersson类WP (s1)，并且对Takhtajan-Teo[40]引入的WP （s1）的Hilbert流形结构是连续可微的。第一个断言已经在我们之前的论文b[36]中得到了证明。在b[36]的续集中，我们将继续处理Weil-Petersson类WP (s1)，并肯定地彻底解决这个猜想。
Given a continuous vector field λ (t,⋅) of Sobolev class H 3 2 on the unit circle S 1, the flow maps η= g (t,⋅) of the differential equation {d η d t= λ (t, η) η (0, ζ)= ζ are known to be quasisymmetric homeomorphisms. Very recently, Gay-Balmaz-Ratiu [15] conjectured that the flow curve g (t,⋅) is in the Weil-Petersson class WP (S 1) and is continuously differentiable with respect to the Hilbert manifold structure of WP (S 1) introduced by Takhtajan-Teo [40]. The first assertion had already been demonstrated in our previous paper [36]. In this sequel to [36], we will continue to deal with the Weil-Petersson class WP (S 1) and completely solve this conjecture in the affirmative.