A Reilly type inequality for the first eigenvalue of Finsler submanifolds in Minkowski space (Q2502298)

Let \((M,F)\) be a compact Finsler submanifold of a Minkowski space \(V\). The aim of the present paper is to study the first eigenvalue \(\lambda _{1}^{\sigma }\) of \(M\) with respect to a Finsler volume form \(\sigma \). More precisely, an extrinsic upper bound for \(\lambda _{1}^{\sigma }\) is provided such that when \(V\) is Euclidean the given result is exactly the standard Reilly inequality for isometric immersions of compact Riemannian manifolds into Euclidian spaces.