Analysing the Wu metric on a class of eggs in ℂn - II
Proceedings of the Indian Academy of Sciences: Mathematical Sciences
We study the Wu metric for the non-convex domains of the form E2m = (z ∈ ℂn: |z1|2m + |z2|2 + · · · + |zn-1|2 + |zn|2 < 1), where 0 < m < 1/2. We give explicit expressions for the Kobayashi metric and the Wu metric on such pseudoeggs E2m. We verify that the Wu metric is a continuous Hermitian metric on E2m, real analytic everywhere except along the complex hypersurface Z = ((0, z2, . . . , zn) ∈ E2m). We also show that the holomorphic curvature of the Wu metric for this noncompact family of pseudoconvex domains is bounded above in the sense of currents by a negative constant independent of m. This verifies a conjecture of S. Kobayashi and H. Wu for such E2m.
Balakumar, G. P. and Mahajan, Prachi, "Analysing the Wu metric on a class of eggs in ℂn - II" (2017). Journal Articles. 2534.