Induced invariant Finsler metrics on quotient groups.
Induced vector fields and metric transformations.
Intrinsic measures complex manifolds
Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras.
Isometry invariant Finsler metrics on Hilbert spaces
In this paper we study isometry-invariant Finsler metrics on inner product spaces over or , i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new proof of the analytic description of all such metrics. In this article the most general concept of the Finsler metric is considered without any additional assumptions that are usually built into its definition. However, we present refined versions of the described results for more specific...
Iterates of maps which are non-expansive in Hilbert's projective metric
The cycle time of an operator on gives information about the long term behaviour of its iterates. We generalise this notion to operators on symmetric cones. We show that these cones, endowed with either Hilbert’s projective metric or Thompson’s metric, satisfy Busemann’s definition of a space of non- positive curvature. We then deduce that, on a strictly convex symmetric cone, the cycle time exists for all maps which are non-expansive in both these metrics. We also review an analogue for the Hilbert...