Eigenvalue control for a Finsler-Laplace operator (Q2376974)

The authors extend several Riemannian results regarding eigenvalue control for the Laplace-Beltrami operator to the Finslerian context, using a new generalization of this operator. They prove that two bi-Lipschitz Finsler metrics have a controlled spectrum and hence the spectrum of Finsler surfaces is controlled from above by a constant depending on the topology of the surface and on the quasireversibility of the metric. They also give examples of highly non-reversible metrics on surfaces with arbitrarily large first eigenvalue.