Isoperimetric inequalities and Dirichlet functions of Riemann surfaces

• Autores: José María Rodríguez
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 38, Nº 1, 1994, págs. 243-253
• Idioma: inglés
• DOI: 10.5565/publmat_38194_19
• Títulos paralelos:
  • Desigualdades isoperimétricas y funciones de Dirichlet de superficies de Riemann
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• Resumen

  • We prove that if a Riemann surface has a linear isoperimetric inequality and verifies an extra condition of regularity, then there exists a non-constant harmonic function with finite Dirichlet integral in the surface.

    We prove too, by an example, that the implication is not true without the condition of regularity.

    We prove that if a Riemann surface has a linear isoperimetric inequality and verifies an extra condition of regularity, then there exists a non-constant harmonic function with finite Dirichlet integral in the surface.

    We prove too, by an example, that the implication is not true without the condition of regularity.