Isoperimetric inequalities and Dirichlet functions of Riemann surfaces
Article Sidebar
Main Article Content
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.
Article Details
How to Cite
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.
Most read articles by the same author(s)
- J. M. Rodríguez, Two remarks on Riemann surfaces , Publicacions Matemàtiques: Vol. 38 No. 2 (1994)
- J. M. Rodríguez, E. Tourís, A new characterization of Gromov hyperbolicity for negatively curved surfaces , Publicacions Matemàtiques: Vol. 50 No. 2 (2006)