Isoperimetric inequalities and Dirichlet functions of Riemann surfaces.
Rodríguez, José M.
Publicacions Matemàtiques, Tome 38 (1994), p. 243-253 / Harvested from Biblioteca Digital de Matemáticas
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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.

Publié le : 1994-01-01
DMLE-ID : 3736 
@article{urn:eudml:doc:41191,
     title = {Isoperimetric inequalities and Dirichlet functions of Riemann surfaces.},
     journal = {Publicacions Matem\`atiques},
     volume = {38},
     year = {1994},
     pages = {243-253},
     mrnumber = {MR1291966},
     zbl = {0813.30034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41191}
}

Rodríguez, José M. Isoperimetric inequalities and Dirichlet functions of Riemann surfaces.. Publicacions Matemàtiques, Tome 38 (1994) pp. 243-253. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41191/