论文标题
在schrödinger方程下的奇异性的传播在带有末端的流形上
Propagation of singularities under Schrödinger equations on manifolds with ends
论文作者
论文摘要
我们证明了Schrödinger方程对歧管的微局部平滑作用。我们采用ITO和Nakamura引入的径向均匀的波前集（Amer。J.Math。，2009）。就径向均匀的波前组而言，我们可以将我们的理论应用于渐近的圆锥形和双曲线歧管。我们将初始状态的波前集与在时间发展后在状态中的径向均匀波前置相关联。我们还证明了径向均匀的波前套件与均匀的波前套件之间的关系，并证明了Nakamura（2005）的特殊情况。
We prove a microlocal smoothing effect of Schrödinger equations on manifolds. We employ radially homogeneous wavefront sets introduced by Ito and Nakamura (Amer. J. Math., 2009). In terms of radially homogeneous wavefront sets, we can apply our theory to both of asymptotically conical and hyperbolic manifolds. We relate wavefront sets in initial states to radially homogeneous wavefront sets in states after a time development. We also prove a relation between radially homogeneous wavefront sets and homogeneous wavefront sets and prove a special case of Nakamura (2005).
