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Isoperimetric inequalities and Dirichlet functions of Riemann surfaces
1994
Publicacions matemàtiques
A,bstract We prove that if a Riemann surface has a linear isoperimetric inequality and verifies an extra condition of regularity, then ther e exists a nonconstant harmonic function with finite Dirichlet integral in the surface . We prove too, by an example, that the implication is not tru e without the condition of regularity.
doi:10.5565/publmat_38194_19
fatcat:kmferx56ijf6fiaacvpshpcpki