Extremal and stationary discs for the Kobayashi \(k\)-metric (Q2225021)

The authors prove that the stationarity condition introduced by the first two authors in [J. Geom. Anal. 25, No. 4, 2516--2545 (2015; Zbl 1334.32009)] is the Euler-Lagrange equation corresponding to the higher-order Kobayashi extremal problem on bounded domains in \(\mathbb C^n\) defined by \(\mathcal C^2\) smooth plurisubharmonic function. They also show that on the smooth strictly convex domains in \(\mathbb C^n\) any generalized stationary disc is locally extremal for the higher-order Kobayashi metric.