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April 2017 Hyperbolic span and pseudoconvexity
Sachiko Hamano, Masakazu Shiba, Hiroshi Yamaguchi
Kyoto J. Math. 57(1): 165-183 (April 2017). DOI: 10.1215/21562261-3759558

Abstract

A planar open Riemann surface R admits the Schiffer span s(R,ζ) to a point ζR. M. Shiba showed that an open Riemann surface R of genus one admits the hyperbolic span σH(R). We establish the variation formulas of σH(t):=σH(R(t)) for the deforming open Riemann surface R(t) of genus one with complex parameter t in a disk Δ of center 0, and we show that if the total space R=tΔ(t,R(t)) is a two-dimensional Stein manifold, then σH(t) is subharmonic on Δ. In particular, σH(t) is harmonic on Δ if and only if R is biholomorphic to the product Δ×R(0).

Citation

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Sachiko Hamano. Masakazu Shiba. Hiroshi Yamaguchi. "Hyperbolic span and pseudoconvexity." Kyoto J. Math. 57 (1) 165 - 183, April 2017. https://doi.org/10.1215/21562261-3759558

Information

Received: 4 December 2015; Revised: 12 February 2016; Accepted: 15 February 2016; Published: April 2017
First available in Project Euclid: 11 March 2017

zbMATH: 1371.32008
MathSciNet: MR3621784
Digital Object Identifier: 10.1215/21562261-3759558

Subjects:
Primary: 32G15, 32Txx
Secondary: 30FXX, 32E10

Rights: Copyright © 2017 Kyoto University

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Vol.57 • No. 1 • April 2017
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