6533b857fe1ef96bd12b4e92

RESEARCH PRODUCT

Boundary rigidity for Randers metrics

Keijo Mönkkönen

subject

Mathematics - Differential GeometryInverse problemsboundary rigidityMathematical analysisBoundary (topology)Rigidity (psychology)ArticlesInverse problemtravel time tomography53C24 53A35 86A22Seismic waveDifferential Geometry (math.DG)Norm (mathematics)Metric (mathematics)FOS: MathematicsMathematics::Metric GeometryMathematics::Differential GeometryMathematics::Symplectic GeometryMathematics

description

If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for Randers metrics where the reversible Finsler norm is induced by a Riemannian metric which is boundary rigid. Our theorems generalize Riemannian boundary rigidity results to some non-reversible Finsler manifolds. We provide an application to seismology where the seismic wave propagates in a moving medium.

yearjournalcountryeditionlanguage
2021-12-01Annales Fennici Mathematici
https://doi.org/10.54330/afm.112492