The Weyl principle on the Finsler frontier

Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz–Killing valuations. They date back remarkable discovery H. Weyl that coefficients tube volume polynomial are invariants metric. As consequence, behave naturally under isometric immersions. This phenomenon, subsequently observed in number different geometric settings, is commonly referred principle. In general normed spaces, Holmes–Thompson extend Euclidean volumes. The purpose this note investigate applicability principle Finsler manifolds. We show while fails, weak form unexpectedly persists certain settings.