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

In this paper, we study a class of singular double phase problems defined on Minkowski spaces in terms Finsler manifolds and with right-hand sides that allow certain type critical growth for such problems. Under very general assumptions based variational tools prove the existence at least one nontrivial weak solution problem. This is first work dealing operator even nonsingular case.

We develop the theory of weighted Ricci curvature in a Lorentz-Finsler framework and extend classical singularity theorems general relativity. In order to reach this result, we generalize Jacobi, Riccati Raychaudhuri equations Finsler spacetimes study their implications for existence conjugate points along causal geodesics. also show version Bonnet-Myers theorem based on generalized Bishop ineq...

In a series of papers ([2, 3, 4]) the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. These relations were called in [4] Stationary-to-Randers Correspondence (SRC). In this paper we focus on one aspect of SRC, the equality between the index of a geodesic in a Randers space and that...

We establish the Bonnet-Myers theorem, Laplacian comparison and Bishop-Gromov volume theorem for weighted Finsler manifolds as well spacetimes, of Ricci curvature bounded below by using weight function. These theorems are formulated with $\epsilon$-range introduced in our previous paper, that provides a natural viewpoint interpolating conditions different effective dimensions. Some results new ...