Isoperimetric inequalities and Dirichlet functions of Riemann surfaces

J. M. Rodríguez
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