论文标题
Riemannian Anosov扩展和应用
Riemannian Anosov extension and applications
论文作者
论文摘要
令$σ$为具有严格凸球边界的Riemannian歧管。假设没有共轭点并且被困的集合是双曲线，我们表明$σ$可以等法地嵌入具有Anosov Geodesic流的封闭的Riemannian歧管中。我们使用此嵌入来提供Anosov流的经典Livshits定理与X射线变换的Livshits定理之间的直接链接，该定理出现在边界刚度程序中。另外，我们在保形类别中提出了晶状体刚性的应用。
Let $Σ$ be a Riemannian manifold with strictly convex spherical boundary. Assuming absence of conjugate points and that the trapped set is hyperbolic, we show that $Σ$ can be isometrically embedded into a closed Riemannian manifold with Anosov geodesic flow. We use this embedding to provide a direct link between the classical Livshits theorem for Anosov flows and the Livshits theorem for the X-ray transform which appears in the boundary rigidity program. Also, we give an application for lens rigidity in a conformal class.
