Local boundary rigidity of a compact Riemannian manifold with curvature bounded above
By Christopher Croke, Nurlan S. Dairbekov, Vladimir A. Sharafutdinov. 2000
65 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6e8df9443324c81f8c627b4cf629282fda3cf284
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Gunther Uhlmann
- Plamen Stefanov
- András Vasy
- Matti Lassas
- D. Burago
- Sergei Ivanov
- Vladimir A. Sharafutdinov
- Mikko Salo
In Computational Theory and Mathematics
- Gunther Uhlmann
- Plamen Stefanov
- Matti Lassas
- András Vasy
- D. Burago
- Sergei Ivanov
- Mikko Salo
- Katya Krupchyk
In Mathematical Physics
- Gunther Uhlmann
- Plamen Stefanov
- András Vasy
- Matti Lassas
- D. Burago
- Sergei Ivanov
- Mikko Salo
- Katya Krupchyk
Citations in the corpus
- The geodesic X-ray transform with fold caustics (2010, unknown): “, [17, 3, 4, 24, 22, 26].”
- Boundary rigidity and filling volume minimality of metrics close to a flat one (2010, background): “There are many more examples of locally rigid metrics: for instance, simple almost nonpositively curved metrics and simple analytic metrics are locally rigid [10], [19].”
- Semiglobal boundary rigidity for Riemannian metrics (2003, background): “Only recently some local results were obtained in [7] and [19] in which one assumes that the metric is a-priori close to a given metric.”
- Boundary rigidity and stability for generic simple metrics (2004, methodology): “This estimate was used in [ CDS ] to get local uniqueness results for the boundary rigidity problem under the same condition.”
- Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge (2017, background): “Several local (in the metric) results near the Euclidean metric are known [31], [6]; in [14] one of the metrics is close to a flat and the other one has an explicit curvature bound; and in [2], one of the metrics is a priori close to the flat one and the other one is arbitrary.”
- Integral Geometry of Tensor Fields on a Class of Non-Simple Riemannian Manifolds (2006, unknown): “We are motivated here by the boundary rigidity problem: to recover g, up to an isometry leaving ∂M fixed, from knowledge of the boundary distance function ρ(x, y) for a subset of pairs (x, y) ∈ ∂M × ∂M, see e.g., [Mi, Sh1, CDS , SU4, PU].”
- Inverse problems: seeing the unseen (2014, background): “By [47], there is a metric h isometric to ĝ so that h is solenoidal w.”