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Griffiths extremality, interpolation of norms, and K\"ahler quantization by Darvas, Tamás; Wu, Kuang-Ru is a scholarly article available to read on EtoBox.

What is Griffiths extremality, interpolation of norms, and K\"ahler quantization about?

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

Author

Darvas, Tamás; Wu, Kuang-Ru

Published

2019

Language

EN