Inverse problem for compact Finsler manifolds with the boundary distance map

12 Jan 2019  ·  De Hoop Maarten V., Ilmavirta Joonas, Lassas Matti, Saksala Teemu ·

We prove that the boundary distance map of a smooth compact Finsler manifold with smooth boundary determines its topological and differential structures. We construct the optimal fiberwise open subset of its tangent bundle and show that the boundary distance map determines the Finsler function in this set but not in its exterior... If the Finsler function is fiberwise real analytic, it is determined uniquely. We also discuss the smoothness of the distance function between interior and boundary points. read more

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Differential Geometry