Boundary rigidity for Randers metrics
Mönkkönen, K. (2022). Boundary rigidity for Randers metrics. Annales Fennici Mathematici, 47(1), 89-102. https://doi.org/10.54330/afm.112492
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Annales Fennici MathematiciAuthors
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2022Discipline
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsCopyright
© 2021 Annales Fennici Mathematici
Jos ei-reversiibeli Finsler-normi on summa reversiibelistä Finsler-normista ja suljetusta 1-muodosta, niin 1-muodon voi määrätä reunaetäisyysdatasta potentiaalikenttiä vaille yksikäsitteisesti. Osoitamme myös reunajäykkyystuloksen Randers-metriikoille, missä reversiibeli Finsler-normi on reunajäykän Riemannin metriikan indusoima. Lauseemme yleistävät Riemannilaisia reunajäykkyystuloksia joillekin ei-reversiibeleille Finsler-monistoille. Tarjoamme sovelluksen seismologiaan, missä seisminen aalto etenee liikkuvassa väliaineessa. 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.
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