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Bergman interpolation on finite Riemann surfaces. Part I: asymptotically flat case

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Abstract

The article considers the Bergman space interpolation problem on open Riemann surfaces obtained from a compact Riemann surface by removing a finite number of points. Such a surface is equipped with what we call an asymptotically flat conformal metric, i.e., a complete metric with zero curvature outside a compact subset. Sufficient conditions for interpolation in weighted Bergman spaces over asymptotically flat Riemann surfaces are then established. When the weights have curvature that is quasi-isometric to the asymptotically flat boundary metric, these sufficient conditions are shown to be necessary, unless the surface has at least one cylindrical end, in which case, the necessary conditions are slightly weaker than the sufficient conditions.

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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794 3651, USA

    Dror Varolin

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  1. Dror Varolin
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Correspondence to Dror Varolin.

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Varolin, D. Bergman interpolation on finite Riemann surfaces. Part I: asymptotically flat case. JAMA 136, 103–149 (2018). https://doi.org/10.1007/s11854-018-0057-4

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  • DOI: https://doi.org/10.1007/s11854-018-0057-4

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