Semiglobal boundary rigidity for Riemannian metrics

By Matti Lassas, Vladimir A. Sharafutdinov, Gunther Uhlmann. 2003

89 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b55b8c8f25422d5c0ae8b870e29b273a84ab14af

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge (2017, background): “ng @Msuch that the pull back of ^gby this dieomorphism agrees with gto innite order at K. For a more general result not requiring convexity, see [28]. Concretely, the local statement is: Lemma 7.1 ([12]). Let @M be convex at pwith respect to gand ^g. Let d= d~ on @M @M near (p;p). Then there exists ”
Stability estimates for the X-ray transform of tensor fields and boundary rigidity (2004, methodology): “This result was used in [ LSU ] to prove a semiglobal solvability result.”
Lens rigidity for manifolds with hyperbolic trapped set (2014, unknown): “n problem can be solved in a conformal class. 1.4. Comments. 1) First, we notice that the assumption g= g′ on T∂Min Theorem 3 is not a serious one and could be removed by standard arguments since, by [LSU], the length function near ∂0SM:= {(x,v) ∈ ∂SM;hν,vi = 0} determines the metric on T∂M(we would”
Inverse problems: seeing the unseen (2014, methodology): “If one metric is close to the Euclidean metric boundary rigidity was proven in [123] that was improved in [36].”
Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map (2004, background): “... some pull backs i gi of gi, i D 1;2, with i as above, we require that i gi be"0-close to g0. One can also study orbits of metrics under actions of such diffeomorphisms and express that condition as distance between the orbits of g1, g2. We remark also that the a-priori condition on boundedness o”
Rigidity of broken geodesic flow and inverse problems (2007, background): “The classical boundary rigidity problem is the following (see [13], [14], [17], [19], [30], [35], [36], [37], [40], [41]): Assume that we know the distances dist(x, y) of boundary points x, y ∈ ∂M.”