Once-holed tori embedded in Riemann surfaces

• Autores: Makoto Masumoto
• Localización: Mathematische zeitschrift, ISSN 0025-5874, Vol. 257, Nº. 2, 2007, págs. 453-464
• Idioma: inglés
• DOI: 10.1007/s00209-007-0142-3
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• Resumen

  • Once-holed tori are the most primitive noncompact Riemann surfaces of positive genus, and consitute a partially ordered set, the order being defined in terms of conforaml embeddings. We consider some families of once-holed tori that are conformally embedded in target Riemann surfaces of conformal mappings of a given noncompact Riemann surface of genus one, and establish an analogue of the one-quarter theorem of Koebe. We also investigate families of once-holed tori conformally embedded in a Riemann surface of positive genus.