Isoperimetric inequalities and Dirichlet functions of Riemann surfaces
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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.
We prove too, by an example, that the implication is not true without the condition of regularity.
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Rodríguez, J. M. “Isoperimetric inequalities and Dirichlet functions of Riemann surfaces”. Publicacions Matemàtiques, vol.VOL 38, no. 1, pp. 243-5, https://raco.cat/index.php/PublicacionsMatematiques/article/view/37804.
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