Аннотация:
In a recent joint work with David Kalaj, we introduced a Finsler pseudometric on any domain in the real Euclidean space Rn, n⩾3, defined in terms of conformal harmonic discs, by analogy with Kobayashi's pseudometric on
complex manifolds which is defined in terms of holomorphic discs. On the unit ball of Rn this minimal metric coincides with the classical Beltrami–Cayley–Klein metric. In this talk, I will describe several sufficient conditions for a domain in Rn to be (complete) hyperbolic, meaning that the minimal pseudometric is a (complete) metric.
(Joint work with Barbara Drinovec Drnovsek, University of Ljubljana.)