Determining a Metric by Boundary Single-Time FlowE nergy
Keywords:
potentialcurves,leastsquaresLagrangian,single-raytransform,boundaryenergy.Abstract
Our theory of determiningat ensorbysin gle-timeflowe nergyissimila rtothosede velopedby Sharafutdinov. Section1refine sthetheoryofpote ntialcurvesd etermin edbyaflo wand a Riemannian metric.Section2definestheboundaryenergyofapotentialcurveandprovesthattheproblemof determiningametricfromasingle-timeflowboundaryenergycannothaveauniquesolution.Section3 linearizestheabove-mentionedproblemanddefinesthenotionofsingle-raytransform.
References
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