Two remarks on Riemann surfaces

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J. M. Rodríguez
We study the relationship between linear isoperimetric inequalities and the existence of non-constant positive harmonic functions on Riemann surfaces.

We also study the relationship between growth conditions of length of spheres and the existence of Green's function on Riemann surfaces.

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Rodríguez, J. M. “Two remarks on Riemann surfaces”. Publicacions Matemàtiques, vol.VOL 38, no. 2, pp. 463-77, https://raco.cat/index.php/PublicacionsMatematiques/article/view/37819.