Isoperimetric inequalities and Dirichlet functions of Riemann surfaces.
José M. Rodríguez (1994)
Publicacions Matemàtiques
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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.