N. Young

collaborators

2 papers

math.CV2022

Nonuniqueness of Carathéodory extremal functions on the symmetrized bidisc

Jim Agler, Zinaida Lykova, N. J. Young

We survey the Carathéodory extremal problem $Car δ$ on the symmetrized bidisc $G = {(z + w, z w) : ∣ z ∣ < 1, ∣ w ∣ < 1} = {(s, p) \in C^{2} : ∣ s - s ˉ p ∣ < 1 - ∣ p ∣^{2}} .$ W…

math.DG2020

Intrinsic Directions, Orthogonality and Distinguished Geodesics in the Symmetrized Bidisc

Jim Agler, Zinaida Lykova, N. J. Young

The symmetrized bidisc \[ G \stackrel{\rm{def}}{=}\{(z+w,zw):|z|<1,\ |w|<1\}, \] under the Carathéodory metric, is a complex Finsler space of cohomogeneity $1$ in which the geodesi…