Hyperbolic domains in real Euclidean spaces

Fecha: 1 de abril de 2022.
Lugar: Seminario 1 del Instituto de Matemáticas de la UGR (IMAG).
Acceso Online: Sala Einstein UGR con contraseña 207295.
Hora: de 12h a 13:30h. 

Impartida por: Franc Forstnerič. 

Resumen: In a recent joint work with David Kalaj (2021), we introduced a new Finsler pseudometric on any domain in the real Euclidean space Rn for n≥3 defined in terms of conformal harmonic discs, by analogy with the Kobayashi pseudometric on complex manifolds. This “minimal pseudometric” describes the maximal rate of growth of hyperbolic conformal minimal surfaces in a given domain. On the unit ball, the minimal metric coincides with the classical Beltrami-Cayley-Klein metric. I will discuss sufficient geometric conditions for a domain to be (complete) hyperbolic, meaning that its minimal pseudometric is a (complete) metric.