Local lens rigidity with incomplete data for a class of non-simple Riemannian manifolds
| dc.creator | Stefanov, Plamen | |
| dc.creator | Uhlmann, Gunther | |
| dc.date | 2007-01-21 | |
| dc.date.accessioned | 2026-07-07T07:42:22Z | |
| dc.date.available | 2026-07-07T07:42:22Z | |
| dc.description | Let $σ$ be the scattering relation on a compact Riemannian manifold $M$ with non-necessarily convex boundary, that maps initial points of geodesic rays on the boundary and initial directions to the outgoing point on the boundary and the outgoing direction. Let $\ell$ be the length of that geodesic ray. We study the question of whether the metric $g$ is uniquely determined, up to an isometry, by knowledge of $σ$ and $\ell$ restricted on some subset $D$. We allow possible conjugate points but we assume that the conormal bundle of the geodesics issued from $D$ covers $T^*M$; and that those geodesics have no conjugate points. Under an additional topological assumption, we prove that $σ$ and $\ell$ restricted to $D$ uniquely recover an isometric copy of $g$ locally near generic metrics, and in particular, near real analytic ones. | |
| dc.identifier | https://arxiv.org/abs/math/0701595 | |
| dc.identifier | http://arxiv.org/abs/math/0701595 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122418 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C24; 53C65 | |
| dc.title | Local lens rigidity with incomplete data for a class of non-simple Riemannian manifolds | |
| dc.type | text |