Nonlinear Dynamics

, Volume 44, Issue 1–4, pp 243–250 | Cite as

The First Eigenvalue of the Laplacian and the Conductance of a Compact Surface

  • Clara Grácio
  • J. Sousa Ramos


We present some results whose central theme is the phenomenon of the first eigenvalue of the Laplacian and conductance of the dynamical system. Our main tool is a method for studying how the hyperbolic metric on a Riemann surface behaves under deformation of the surface. With this model, we show that there are variation of the first eigenvalue of the laplacian and the conductance of the dynamical system, with the Fenchel–Nielsen coordinates, that characterize the surface.

Key Words

conductance Fenchel–Nielsen coordinates First eigenvalue of the Laplacian hyperbolic metric Riemann surface 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade de ÉvoraÉvoraPortugal
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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