Griffiths Extremality, Interpolation of Norms, and Kähler Quantization

Following Kobayashi, we consider Griffiths negative complex Finsler bundles, naturally leading us to introduce extremal metrics. As point out, this notion is closely related the theory of interpolation norms, and characterized by an equation Monge–Ampère type, whose corresponding Dirichlet problem solve. applications, prove that metrics quantize solutions a natural PDE in Kähler geometry, construction flat maps for Mabuchi metric.