The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal
boundary are surveyed and revisited, starting at the seminal conformal boundary …

The topic which served as the starting point for this investigation is the “global” geometry of
periodic metrics. We call periodic a Riemannian metric ρ on a complete manifold M …

In this paper, we find a relation between the norm of Cartan and mean Cartan torsions of
Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. Then, we find a …

The main" unconditional" result of this paper, Theorem 3, states that every two-dimensional
affine disc in a normed space (that is, a disc contai in a two-dimensional affine subspace) is …

We study the differentiability of the stable norm"." associated with a Zn periodic metric on Rn.
Extending one of the main results of [Ba2], we prove that if p∈ Rn and the coordinates of p …

Methods of estimating (Riemannian and Finsler) filling volumes by using nonexpanding
maps to Banach spaces of $ L^\infty $-type are developed and generalized. For every …

This chapter is an unorthodox survey of Finsler geometry presenting both results and open
problems. It aims to show that recent progress in convex geometry, the calculus of variations …

Z. Shen proved that Finsler manifold with unbounded Cartan torsion can not be isometrically
imbedded into any Minkowski space. This shows that the norm of Cartan torsion of Finsler …

In the present paper we study the relationships between different concepts of convex
structures in metric spaces that that are related to the works of K. Menger [Menger, K …

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 …