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Variation of Bergman metrics on Riemann surfaces

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Abstract.

We study the variation of the Berman metric K(t,ζ)|dζ|2 on the Riemann surface R(t) (which varies with complex parameter t in a disk B) such that π:→B is a 2-dimensional Stein space with π−1(t)=R(t),t ∈ B. We show that log K(t,ζ)|dζ|2 is plurisubharmonic in , and apply it to give the uniformization condition for the special Stein space.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto Institute of Technology, Kyoto, 606-8585, Japan

    Fumio Maitani

  2. Department of Mathematics, Nara Women’s University, Nara, 630-8506, Japan

    Hiroshi Yamaguchi

Authors
  1. Fumio Maitani
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  2. Hiroshi Yamaguchi
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Corresponding author

Correspondence to Fumio Maitani.

Additional information

Revised version: 18 February 2004

Mathematics Subject Classification (2000): 30C85, 30F15, 32F05, 32H10

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Maitani, F., Yamaguchi, H. Variation of Bergman metrics on Riemann surfaces. Math. Ann. 330, 477–489 (2004). https://doi.org/10.1007/s00208-004-0556-8

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  • DOI: https://doi.org/10.1007/s00208-004-0556-8

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