Journal d'Analyse Mathématique

, Volume 129, Issue 1, pp 69–90 | Cite as

Holomorphic mappings of once-holed tori

  • Makoto MasumotoEmail author


Let T be the space of marked once-holed tori and Y 0 be a Riemann surface with marked handle. We investigate geometric properties of the set T a [Y 0] of X ∈ T that allow holomorphic mappings of X into Y 0. We also examine the set T c [Y 0] of marked once-holed tori conformally embedded into Y 0. It turns out that T a [Y 0] and T c [Y 0] have several properties in common. Our basic tool is a new notion, called a handle condition.


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© Hebrew University Magnes Press 2016

Authors and Affiliations

  1. 1.Department of MathematicsYamaguchi UniversityYamaguchiJapan

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