标题： 关于渐近双曲流形的逆散射问题与共形拉普拉斯算子的Calderón问题之间的相互作用 显示英文标题

标题： On the interplay between inverse scattering for asymptotically hyperbolic manifolds and the Calderón problem for the Conformal Laplacian

摘要： 在本简短的注释中，我们利用Guillarmou--Guillopé和Chang--González之间关于渐近双曲（AH）流形的广义特征值问题与共形拉普拉斯算子之间的关系，得到一个新的逆散射结果：在维度为$n+1$的AH流形上，我们证明能量为$\frac{n+1}{2}$的散射矩阵确定了边界上的度量的喷子，直到微分同胚和共形因子。 显示英文摘要

摘要： In this short note, we use the relation obtained by Guillarmou--Guillop\'e and Chang--Gonz\'alez between the generalized eigenvalue problem for asymptotically hyperbolic (AH) manifolds and the Conformal Laplacian, to obtain a new inverse scattering result: on an AH manifold of dimension $n+1$, we show that the scattering matrix at energy $\frac{n+1}{2}$ determines the jet of the metric on the boundary, up to a diffeomorphism and conformal factor.