Displaying similar documents to “Isoperimetric inequalities in Riemann surfaces of infinite type.”

Isoperimetric inequalities and Dirichlet functions of Riemann surfaces.

José M. Rodríguez (1994)

Publicacions Matemàtiques

Similarity:

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.

Two remarks on Riemann surfaces.

José M. Rodriguez (1994)

Publicacions Matemàtiques

Similarity:

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 and the existence of Green's function on Riemann surfaces.

Isospectral Riemann surfaces

Peter Buser (1986)

Annales de l'institut Fourier

Similarity:

We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus g = 5 and for all g ≥ 7 . In a second part we give examples of isospectral non isometric surfaces in R 3 which are realizable by paper models.

Riemann surfaces with boundary and natural triangulations of the Teichmüller space

Gabriele Mondello (2011)

Journal of the European Mathematical Society

Similarity:

We compare some natural triangulations of the Teichmüller space of hyperbolic surfaces with geodesic boundary and of some bordifications. We adapt Scannell–Wolf’s proof to show that grafting semi-infinite cylinders at the ends of hyperbolic surfaces with fixed boundary lengths is a homeomorphism. This way, we construct a family of equivariant triangulations of the Teichmüller space of punctured surfaces that interpolates between Bowditch–Epstein–Penner’s (using the spine construction)...