• Analysing the Wu metric on a class of eggs in $\mathbb{C}^{n} – \rm{II}$

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    • Keywords


      Wu metric; Kobayashi metric; negative holomorphic curvature

    • Abstract


      We study the Wu metric for the non-convex domains of the form $E_{2m}= \{z \in \mathbb{C}^n : \mid z_1\mid ^{2m} + \mid z_2\mid ^2 +\cdots +\mid z_{n−1}\mid^2 + \mid z_n \mid^2$ < $1\}$, where 0 < m < 1/2. We give explicit expressions for the Kobayashi metric and the Wu metric on such pseudo-eggs $E_{2m}$. We verify that the Wu metric is a continuous Hermitian metric on $E_{2m}$, real analytic everywhere except along the complex hypersurface $Z = \{(0, z_{2}, . . . , z_{n}) \in E_{2m}\}$. We also show that the holomorphic curvature of the Wu metric for this noncompactfamily 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 $E_{2m}$.

    • Author Affiliations



      1. Indian Statistical Institute, Chennai 600 113, India
      2. Department of Mathematics, Indian Institute of Technology – Bombay, Mumbai 400 076, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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